From noise to turning points: A new framework for seasonal adjustment in Armenia

Minasyan, Gevorg; Schipper, Stefan; Khachatryan, Lusya; Movsisyan, Seda; Lapitan, Pamela Working Paper From noise to turning points: A new framework for seasonal adjustment in Armenia ADB Economics Working Paper Series, No. 786 Provided in Cooperation with: Asian Development Bank (ADB), Manila Suggested Citation: Minasyan, Gevorg; Schipper, Stefan; Khachatryan, Lusya; Movsisyan, Seda; Lapitan, Pamela (2025) : From noise to turning points: A new framework for seasonal adjustment in Armenia, ADB Economics Working Paper Series, No. 786, Asian Development Bank (ADB), Manila, https://doi.org/10.22617/WPS250242-2 This Version is available at: https://hdl.handle.net/10419/322379 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/igo/ ASIAN DEVELOPMENT BANK ASIAN DEVELOPMENT BANK 6 ADB Avenue, Mandaluyong City 1550 Metro Manila, Philippines www.adb.org ADB ECONOMICS WORKING PAPER SERIES NO. 786 June 2025 From Noise to Turning Points A New Framework for Seasonal Adjustment in Armenia This paper evaluates the transition to the X13-ARIMA-SEATS framework for the seasonal adjustment of Armenia’s quarterly national accounts, highlighting its role in detecting economic turning points. The paper discusses best practices for seasonal adjustment and strategies for accurate real-time economic analysis. About the Asian Development Bank ADB is a leading multilateral development bank supporting inclusive, resilient, and sustainable growth across Asia and the Pacific. Working with its members and partners to solve complex challenges together, ADB harnesses innovative financial tools and strategic partnerships to transform lives, build quality infrastructure, and safeguard our planet. Founded in 1966, ADB is owned by 69 members—50 from the region. FROM NOISE TO TURNING POINTS A NEW FRAMEWORK FOR SEASONAL ADJUSTMENT IN ARMENIA Gevorg Minasyan, Stefan Schipper, Lusya Khachatryan, Seda Movsisyan, and Pamela Lapitan From the People of Japan ASIAN DEVELOPMENT BANK The ADB Economics Working Paper Series presents research in progress to elicit comments and encourage debate on development issues in Asia and the Pacific. The views expressed are those of the authors and do not necessarily reflect the views and policies of ADB or its Board of Governors or the governments they represent. ADB Economics Working Paper Series Gevorg Minasyan, Stefan Schipper, Lusya Khachatryan, Seda Movsisyan, and Pamela Lapitan No. 786 | June 2025 Gevorg Minasyan ([email protected]) is a consultant; Stefan Schipper ([email protected]) is a principal statistician; and Pamela Lapitan ([email protected]g) is a statistics officer at the Economic Research and Development Impact Department, Asian Development Bank. Lusya Khachatryan (national_acc[email protected]) is head of Macroeconomic Indicators and the National Accounts Division and Seda Movsisyan (seda_movsis[email protected]) is a senior specialist at the Statistical Committee of the Republic of Armenia. From Noise to Turning Points: A New Framework for Seasonal Adjustment in Armenia Creative Commons Attribution 3.0 IGO license (CC BY 3.0 IGO) © 2025 Asian Development Bank 6 ADB Avenue, Mandaluyong City, 1550 Metro Manila, Philippines Tel +63 2 8632 4444; Fax +63 2 8636 2444 www.adb.org Some rights reserved. Published in 2025. 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Corrigenda to ADB publications may be found at http://www.adb.org/publications/corrigenda. ABSTRACT This paper evaluates the transition from X12-ARIMA to X13-ARIMA-SEATS for the seasonal adjustment of Armenia’s quarterly national accounts (QNA). We analyze the methodological advancements and their impact on key economic indicators, focusing on the precision and reliability of seasonally adjusted data. Our findings suggest that the indirect seasonal adjustment method, despite larger revisions, is preferable, given potential variations in seasonal patterns among gross domestic product components and strong user preferences for preserving accounting relationships. Furthermore, a partial concurrent update strategy achieves a better balance between accuracy and revision minimization compared to current or fully concurrent methods. Finally, deriving seasonally adjusted price deflators from seasonally adjusted volume and current price data aligns more closely with the underlying economic structure of Armenian QNA, given that QNA data is available primarily in nominal terms. These results remain consistent across various sensitivity checks, supporting our methodological approach for analyzing Armenia's QNA series. Keywords: Armenia, JDemetra+, national accounts, seasonal adjustment, X13-ARIMA-SEATS JEL codes: C22, C32, C5 _________________________ The grant fund for this study was received from the Japan Fund for Prosperous and Resilient Asia and the Pacific financed by the Government of Japan through the Asian Development Bank. 1. INTRODUCTION Economic variables exhibit systematic and recurring within-year patterns influenced by a variety of factors, such as weather, institutions, and social customs and traditions. When these seasonal variations dominate changes in the original series from one period to another, identifying nonseasonal effects, including long-term movements, cyclical variations, and irregular factors— informative economic signals—becomes challenging. Timely identification of turning points in key macroeconomic variables, like the quarterly national accounts (QNA), requires the removal of seasonal and calendar effects from time series data. This process involves utilizing analytical techniques to break down the series into unobserved components, based on a priori assumptions regarding their expected behavior. Removing the repeated impact of seasonal effects is important for both historical business cycle analysis and assessing current economic conditions. This helps in identifying fundamental longrun movements and short-run fluctuations in the time series, thereby enhancing the interpretation of economic variables and contributing to informed decision making. However, the challenge of precisely defining seasonality means that the different approaches may result in different outcomes. Analyst expertise remains essential for finetuning the seasonal adjustment procedures and verifying the accuracy of the adjusted statistics. Expert-driven judgment is particularly important in the current economic landscape, where linear filters are typically applied for seasonal component extraction despite the prevalence of uncertainties and nonlinear trends in many economic series. The Statistical Committee of the Republic of Armenia (ARMSTAT) initiated its first seasonal adjustment of QNA in 1998, using the autoregressive integrated moving average (ARIMA) X11 method developed by the United States Census Bureau. In 2013, ARMSTAT shifted to the X12ARIMA method and the Demetra+ program,1 aligning with recommendations from the International Monetary Fund (IMF) and the United Nations Economic Commission for Europe. However, X12-ARIMA, while representing an advance on earlier methods, relies heavily on linear models, limiting its ability to capture the nonlinear trends increasingly present in modern economies. Recognizing this limitation, ARMSTAT transitioned to the X13-ARIMA-SEATS method and the JDemetra+ software in 2022, aligning with the European Statistical System (ESS) 2015 guidelines on seasonal adjustment and the IMF's QNA 2017 manual. X13-ARIMA-SEATS offers several advantages over its predecessors. First, it incorporates the SEATS (signal extraction in ARIMA time series) method, specifically designed to handle nonlinear trends and structural breaks in time series data. Second, X13-ARIMA-SEATS provides a more advanced toolkit for diagnosing the quality and stability of seasonal adjustment models. Third, X13-ARIMA-SEATS can efficiently process multiple series simultaneously. In addition, JDemetra+ includes a more versatile interface compared to Demetra+, enabling users to apply tools such as nowcasting, temporal disaggregation, and benchmarking. Importantly, JDemetra+ provides common analysis options for different seasonal adjustment methods, allowing for easy comparison of results across these algorithms. 1 ARIMA is a statistical method for analyzing and forecasting time series data by modeling its temporal structure, and Demetra+ is free software developed by the National Bank of Belgium for seasonal adjustment using TRAMO/SEATS and X12-ARIMA methods. 2 In this paper, we examine the implications of transitioning from the X12-ARIMA to the X13ARIMA-SEATS method for the seasonal adjustment of Armenia's QNA series. Our analysis focuses on assessing the methodological advancements and their impact on the interpretation of key economic indicators, with a particular emphasis on the precision and reliability of seasonally adjusted data in capturing underlying economic trends. Additionally, we conduct a wide range of advanced quality diagnostics to validate the underlying assumptions of the new seasonal adjustment framework and the major decisions regarding various aspects of the methodology. Our findings suggest that the new framework yields significant insights, particularly in the context of direct versus indirect adjustments, update strategies, and the relationship between price, volume, and value indices. While both direct and indirect approaches produce similar trends, notable discrepancies emerge, especially during crisis periods. The indirect method, despite its susceptibility to larger revisions, appears preferable, given the potential for divergent seasonal patterns among gross domestic product (GDP) components and user demand. Additionally, our exploration of update strategies highlights the advantages of a partial concurrent adjustment method, which balances accuracy with the minimization of revisions. Finally, the findings on the relationship between seasonally adjusted price, volume, and value indices indicate that deriving residuals from seasonally adjusted volume and current price data, rather than directly adjusting price deflators, aligns better with the underlying economic structure of the Armenian QNA. These results remain robust across various sensitivity checks, reaffirming the validity of our methodological approach and its applicability to the analysis of the Armenian QNA series. The remainder of this paper is structured as follows: Section 2 reviews the literature on seasonal adjustment methods, Section 3 details the methodology employed, Section 4 presents findings, Section 5 discusses quality diagnostics, Section 6 addresses the pre-adjustment of QNA during the coronavirus disease (COVID-19) crisis, and Section 7 concludes with a summary. 2. LITERATURE REVIEW Seasonal adjustment methods fall into three broad categories: (i) nonparametric methods, which rely on linear smoothing filters to adjust the data; (ii) parametric methods, where seasonal adjustment is achieved through explicit specification and estimation of unobserved components within the data; and (iii) and semiparametric methods, which combine aspects of both explicit and implicit modeling of each component (see Figure 1). 3 Figure 1: Classification of Seasonal Adjustment Methods Source: Eurostat (2018). 2.1. Nonparametric Models The most common seasonal adjustment methods use moving averages or linear smoothing filters to adjust data sequentially by adding and subtracting individual observations. A pioneer in this field was the United States Census Bureau’s X11 program, released in 1965 (Shiskin, Young, and Musgrave 1967). This was the result of over a decade of development, beginning with Method I in 1954 and followed by 12 experimental variants of Method II (X0, X1, etc.), culminating in the release of X11 (Shiskin 1978). Building on the foundation of X11, the Australian Bureau of Statistics introduced SEASABS (Seasonal Analysis at the Australian Bureau of Statistics) in 1987 (Eurostat 2018). This knowledge-based algorithm retains records of previous series analyses, enabling comparisons of X11 diagnostics and insights into the parameters that produced acceptable adjustments. Young (1992) developed another version, GLAS (General Linear Abstraction of Seasonality), at the Bank of England for seasonally adjusting monetary variables. This method estimates and smooths trend and seasonal components with a triangular-shaped weighting pattern in a moving average of data, and it incorporates Lane’s (1972) minimum revision algorithm. Other similar tools include SABL (Seasonal Adjustment-Bell Laboratories) (Cleveland, Dunn, and Terpenning 1978), a robust alternative to X11 that tackles outliers and smooths trends without rigid data assumptions. STL (seasonal and trend decomposition using Loess), developed by Cleveland et al. (1990), functions similarly to GLAS by applying localized smoothing techniques to estimate trend and seasonal components, using adaptable polynomial fits to model both linear and nonlinear patterns. 4 2.2. Parametric Models Some critics expressed concerns about nonparametric seasonal adjustment methods based on linear filters or moving averages. Slutsky (1927) and Yule (1927) noted the potential for these models to introduce artificial cycles, while others criticized the use of ad hoc empirical procedures when more rigorous mathematical tools were available. This growing dissatisfaction with nonparametric approaches led to the development of explicit model-based methodologies for seasonal adjustment. There are two main categories of these model-based approaches: (i) those that rely on deterministic frameworks, and (ii) those grounded in stochastic modeling. Early model-based methods relied on regression analysis. Pioneering works by Fisher (1937) and Mendershausen (1939) used least squares to fit polynomials and isolate seasonality. The 1960s saw a rise in multiple regression techniques, driven by econometric model development and computing advancements. Notable contributions include works by Rosenblatt (1965) and Lovell (1963), which fit components using parametric functions and ordinary least squares. However, their inability to capture the stochastic nature of series has limited their use. Extensions with local regressions, like DAINTIES (Fischer 1995) and BV4 (Nourney 1984), have seen some development, though they face limitations like phase shifts and identification problems. Unlike deterministic methods, stochastic methods rely on specifying unobserved component ARIMA models and applying signal extraction techniques. A key direction is the ARIMA ModelBased (AMB) approach, which models the observed time series using a seasonal ARIMA model, while components are derived from the model’s structure using spectral estimation techniques. Pioneering works in this area include contributions by Maravall and Pierce (1987), Bell (1984), Hillmer and Tiao (1982), and Burman (1980). However, while powerful, ARIMA models are susceptible to inaccuracies caused by outliers and may struggle to correctly estimate deterministic components. To address this limitation, developments like TRAMO-SEATS (Gómez and Maravall 1995) use the Wiener-Kolmogorov filter to extract the components from the spectrum of a fitted ARIMA model by minimizing the mean squared error between the estimated and actual components. Compared with X11, TRAMO-SEATS produces more stable seasonal components by using a canonical decomposition method that maximizes the variability of the irregular element while minimizing that of the seasonal factors. However, it relies heavily on a well-fitting ARIMA model, and results are particularly sensitive to parameter uncertainty, especially in very short or long time series. 2.3. Semiparametric Models Building upon the work of Box and Jenkins (1970) on ARIMA models in the 1970s (see Box et al. 2015), Dagum (1980) proposed a new X11 variant called X11-ARIMA. This represented an improvement over the original X11 program and was further automated at Statistics Canada. The key improvement lies in X11-ARIMA's ability to extend predictions beyond the observed data and estimate values prior to the start of the series. This capability addresses missing data at the series' ends, allowing for less asymmetric filters. In contrast, the original X11 simply extrapolated missing values arbitrarily, leading to significant revisions when the missing data eventually became available. Another extension of X11 is the United Kingdom version, which incorporated forecasts based on the Kenny-Durbin autoregression technique (Kenny and Durbin 1982), though Fischer (1995) found that X11-ARIMA delivered more accurate forecasting results. The Dutch Central Bureau of Statistics also introduced an extension known as CPBX11 software 11 (L). However, most trend-cycle components show insignificant correlations. This suggests that directly adjusting GDP may mask important seasonal variations within individual sectors, potentially compromising the quality of the seasonally adjusted GDP. Figure 3: Chain-Linked Volume Indices (2012 = 100) Source: Authors’ calculations based on QNA data from ARMSTAT. Figure 4: Year-on-Year Growth Rates of Gross Domestic Product Source: Authors’ calculations based on QNA data from ARMSTAT. 60 80 100 120 140 160 180 200 220 Index Original Direct Indirect -15 -10 -5 0 5 10 15 20 % Direct - Indirect Difference (percentage points) Direct Indirect 12 Figure 5: Correlation Matrix of Trend-Cycle Components of Sectoral Value-Added Source: Authors’ calculations. To further investigate the implications of these methods, we conducted a revision analysis on yearon-year GDP growth rates. We employed a recursive estimation approach over the period from 2013Q1 to 2022Q4 and subsequently incorporated additional data points up to 2023Q4. The resulting revisions for 2021, 2022, and 2023 indicate that both direct and indirect methods introduce changes to the seasonally adjusted GDP series. However, the magnitude of revisions tends to be marginally larger under the indirect method, which is evidenced by the higher Mean Squared Error (MSE) values for indirect adjustment across analyzed periods. The larger revisions under the indirect approach likely result from the amplification of noise and inconsistencies arising from the independent adjustment of component series. In contrast, the direct method, which operates on aggregate data, may benefit from a smoothing effect, leading to more stable estimates. Despite the higher revision susceptibility of the indirect method, we preferred it for Armenia, given the potential for divergent seasonal patterns among GDP components and the strong user demand for preserving accounting and aggregation relationships in the QNA data. 13 Table 3: Comparison of Revisions Under Direct and Indirect Seasonal Adjustment (year-on-year changes in seasonally adjusted gross domestic product) 2021 2022 2023 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Direct Adjustment Until MSE 2022Q4 -2.5 9.2 3.4 11.1 8.3 13.1 15.2 12.5 0.86 2023Q1 -2.5 9.3 3.4 11.1 8.3 13.1 15.2 12.5 11.2 2023Q2 -2.5 9.3 3.4 11.1 8.3 13.1 15.2 12.5 11.2 9.5 2023Q3 -2.6 9.2 3.5 11.1 8.2 13.0 15.3 12.5 11.1 9.4 7.8 2023Q4 -2.6 9.2 3.5 11.1 8.2 13.1 15.4 12.5 11.0 9.5 7.8 7.6 Indirect Adjustment Until MSE 2022Q4 -2.5 8.6 3.9 12.4 7.9 12.0 15.8 13.9 1.21 2023Q1 -2.8 8.7 4.0 12.4 7.7 12.1 15.7 13.8 11.3 2023Q2 -2.9 8.9 3.9 12.4 7.7 12.3 15.7 13.8 11.3 9.0 2023Q3 -2.9 9.0 3.8 12.4 7.6 12.4 15.7 13.8 11.3 8.9 7.5 2023Q4 -2.9 9.0 4.1 12.1 7.8 12.4 15.9 13.5 11.4 9.1 7.8 6.6 MSE = mean squared error. Source: Authors’ calculations. 4.2. Strategies for Updating Seasonal Adjustment Seasonal adjustment procedures can follow different updating approaches, depending on the frequency with which the adjustment models and their settings are re-evaluated as new or revised data become available. Two main approaches are mostly used: concurrent or current adjustment. In the concurrent approach, the model, its configuration, and parameters are re-estimated every time new or revised data points are added. This ensures that the adjusted series reflect the latest seasonal patterns and structural changes, typically resulting in the most accurate estimates. However, this strategy tends to produce more frequent revisions to the adjusted data due to ongoing updates to the underlying model and parameters. In contrast, the current adjustment approach updates the model and its components only during predetermined review windows – usually held annually or when significant changes occur in the source data. Between these review periods, the model structure and estimated parameters remain unchanged. Adjusted values are generated by applying projected seasonal and calendar factors to the incoming data. As a result, revisions to the seasonally adjusted series are concentrated within the review periods, with no adjustments made during the interim unless historical source data are modified. A compromise between the concurrent and current seasonal adjustment strategies is the partial concurrent approach. In this method, the choice of models and adjustment settings is fixed during 14 scheduled review periods – usually once per year or following substantial data revisions – and remains constant until the next review. However, the parameters of the model are re-estimated every time the series is updated with new data. While the model and adjustment settings are generally kept unchanged between reviews, they may be revised in response to rare or exceptional circumstances that demand special treatment. Outside of such events, any revisions to the seasonally adjusted data arise solely from the updated parameter estimates. This strategy offers a balanced approach by maintaining a high level of accuracy in the adjustments while reducing the frequency and magnitude of revisions. In Figure 6, we compare the magnitudes of revisions to year-on-year GDP changes across the three approaches. As anticipated, the partial concurrent method generates fewer revisions in estimates compared to the current and concurrent approaches, which lead to larger revisions. For instance, the second quarter of 2023 experienced a 0.3 percentage point revision in the yearon-year GDP change using the current approach, a more substantial 1.1 percentage point revision with the concurrent approach, and a minor -0.1 percentage point revision with the partial concurrent approach. Consequently, ARMSTAT adopted this latter method for seasonally adjusting QNA in Armenia. The model, filters, and outliers within this approach are revised annually, while seasonal factors and calendar effects are updated with each new data release. This approach aligns with the ESS guidelines and the IMF manual on QNA, both of which recommend partial concurrent adjustment to account for new information and minimize the size of revisions resulting from the seasonal adjustment process. Figure 6: Current Versus Concurrent Versus Partial Concurrent Adjustment (revisions to year-on-year gross domestic product growth rates, percentage points) Source: Authors’ calculations. -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2022Q1 2022Q2 2022Q3 2022Q4 2023Q1 2023Q2 2023Q3 2023Q4 Percentage point Partial Concurrent Concurrent Current 15 4.3. Revision Period Another critical aspect of revisions policy is determining the revision period for QNA publications, which defines the number of previously released quarterly observations subject to revision. In a partial concurrent approach, the entire seasonally adjusted series is modified whenever a new observation is added or an existing one is revised. Revisions can be substantial for years near the last revised observation in the original series, but tend to be minor for more distant observations. This pattern arises because seasonal adjustment filters assign greater weight to recent observations compared to those further in the past. According to the IMF’s QNA manual, a partial concurrent adjustment strategy mandates revising seasonally adjusted series for at least 2 complete years prior to modifying the original data. This period enables the inclusion of updated regression coefficients and newly detected outliers into the latest seasonally adjusted data. Maintaining a minimum of 2 full years is crucial for accurately calculating quarter-to-quarter growth rates for the current and preceding year using consistently adjusted data. Seasonally adjusted data published before this 2-year window can remain unchanged unless artificial breaks emerge in the series. Similarly, the ESS guidelines recommend setting the starting point for the earliest seasonally adjusted data revision at the beginning of a year, 3 years before the unadjusted data revision period. To determine an appropriate revision period for Armenia, Figure 7 compares revisions to year-onyear GDP growth rates following the addition of new observations for each quarter of 2023. The analysis reveals that, while recent data significantly impacts the most recent estimates, earlier observations remain relatively stable. Based on these findings, ARMSTAT adopted a revision policy that updates the previous 3 years of data with each new observation, while preserving estimates for earlier periods. The only exception to this revision policy occurred when ARMSTAT transitioned to a new seasonal adjustment framework at the end of 2022. During this period, the entire series was updated compared to the previous methodology, aligning with ESS recommendations for major revisions. Figure 7: Changes in Seasonally Adjusted Estimates by Adding New Observations (revisions to year-on-year gross domestic product growth rates, percentage points) Source: Authors’ calculations. -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 Percentage point 2023Q1 2023Q2 2023Q3 2023Q4 16 4.4. Relationship Between Price, Volume, and Value Indices for Seasonally Adjusted Series Seasonally adjusted estimates for national accounts price indices, volume measures, and current price data can be obtained by either adjusting each series independently or adjusting two and deriving the third as a residual, assuming all three exhibit seasonal patterns. Given nonlinearities in seasonal adjustment processes, these methods produce different results, although the differences are typically minor. As the IMF suggests, deciding which series to derive residually should be determined on a case-by-case basis based on which approach yields the most reasonable outcome. Theoretically, seasonality in current price data is generated by seasonality from price and volume effects. Therefore, the best approach appears to be applying seasonal adjustment to the price and volume series and then indirectly deriving seasonally adjusted data in current prices. However, directly adjusting data in current prices may be preferred when the main data source is available in nominal terms. Before 2022, ARMSTAT seasonally adjusted only the volume indices. However, since adopting the new framework, both volume measures and current price data are seasonally adjusted, while price deflators are derived as residuals. This decision is influenced by the fact that the underlying data for QNA is collected in nominal terms in Armenia, and volume indices are subsequently derived using QNA series at the previous year’s prices through the double deflation method. 5. QUALITY DIAGNOSTICS In this section, we evaluate the quality of the seasonally adjusted series using both parametric and nonparametric criteria. To verify the absence of residual seasonality, we begin by conducting seasonality tests on the directly adjusted series and their irregular components. The residual seasonality tests used in JDemetra+ are derived from the set of diagnostics originally created for X12-ARIMA. Among these, we primarily rely on the F-test, which uses seasonal dummy variables (including a mean effect and three seasonal dummies for quarterly data) to determine whether they are jointly statistically insignificant. The rejection thresholds and test results for this analysis are presented in Tables 4a and 4b. As indicated, the p-values for most series exceed 0.05, confirming the absence of residual seasonality in the individual GDP components. Since the seasonally adjusted QNA series are derived indirectly by aggregating the corresponding subcomponents, we also perform similar tests on the aggregated series. As shown in Appendix C, all aggregated series are free from residual seasonality. Additionally, we conduct analogous tests on the price deflators calculated from seasonally adjusted volume measures and current price data, with results in Appendix C supporting that these series are also devoid of residual seasonality. 17 Table 4a: Critical Values for Interpreting F-Test Results P-value JDemetra+ default settings <0.01 Severe [0.01, 0.05) Bad [0.05, 0.1) Uncertain ≥0.1 Good Source: JDemetra+ Reference Manual (https://jdemetradocumentation.github.io/JDemetradocumentation/). Table 4b: Results of the F-Test for the Presence of Residual Seasonality and Trading-Day Effects NACE Code Residual Seasonality Residual Trading-Day Effects Seasonally adjusted series Irregular component Seasonally adjusted series Irregular component A Good (0.668) Good (0.418) Good (0.079) Good (0.405) B Good (0.921) Good (0.832) Good (0.101) Good (0.134) C Good (0.477) Good (0.446) Good (0.429) Good (0.269) D Good (0.513) Good (0.635) Good (0.905) Good (0.058) E Good (0.768) Good (0.569) Good (0.207) Good (0.779) F Good (0.321) Good (0.222) Good (0.172) Good (0.650) G Good (0.382) Good (0.187) Good (0.493) Good (0.091) H Good (0.985) Good (0.781) Good (0.639) Good (0.240) I Good (0.959) Good (0.568) Good (0.607) Good (0.292) J Good (0.895) Good (0.973) Good (0.371) Good (0.598) K Good (0.938) Good (0.541) Good (0.966) Good (0.328) L Good (0.953) Good (0.958) Good (0.804) Good (0.436) M Good (0.898) Good (0.403) Good (0.255) Good (0.756) N Good (0.728) Good (0.487) Good (0.235) Uncertain (0.024) O Good (0.422) Good (0.446) Good (0.059) Good (0.124) P Good (0.812) Good (0.477) Good (0.131) Good (0.976) Q Good (0.717) Good (0.633) Good (0.216) Good (0.304) R Good (0.814) Good (0.557) Good (0.160) Good (0.059) S Good (0.593) Good (0.397) Good (0.489) Good (0.799) T Good (0.723) Good (0.781) Good (0.091) Uncertain (0.017) Source: Authors’ calculations. We next evaluate the specified RegARIMA models from the pre-adjustment phase using several tests for normality, independence, randomness, and linearity of residuals. Ensuring residuals are normally distributed is important for the accuracy of forecast prediction intervals. To test this, we use the Doornik-Hansen test, which evaluates skewness and kurtosis in multivariate data transformed to achieve independence. The corresponding p-values from this test are presented in column (1) of Table 5. The findings show that residuals from all RegARIMA models conform to a normal distribution, indicating no additional model refinement is required. 18 To check the independence of residuals, we apply the Ljung-Box and Box-Pierce Q-statistics, calculated for both regular and seasonal lags. The regular lag tests evaluate autocorrelation over the first 16 lags, while seasonal lag tests focus on the first two seasonal lags. Assuming the residuals are random, their test statistics should follow a chi-square distribution, with degrees of freedom equal to the number of model parameters. The results of these tests are shown in columns (2) and (3) of Table 5. Since most p-values exceed 0.05, we do not reject the null hypothesis that residuals are independently and identically distributed, supporting the independence assumption. The randomness of the residuals' signs is evaluated using the Wald-Wolfowitz test, also called the Run test. This test analyzes data centered on the mean by counting the number and length of runs – defined as consecutive values all above or all below the mean. An up run consists of successive values above the mean, while a down run consists of successive values below it. The test examines whether these up and down runs are evenly distributed over time, since both an excess and a shortage of runs are unlikely in truly random sequences. It also tests whether the lengths of these runs occur randomly. The outcomes shown in columns (4) and (5) of Table 5 demonstrate that, in our case, the residuals exhibit randomness both in terms of the number of runs around the mean and their average length. Finally, the linearity of residuals test provides evidence of whether there is autocorrelation in residuals or not. Significant values of the Ljung-Box and Box-Pierce Q-statistics of the squared residuals indicate random variation in the coefficients or time-varying conditional variances, leading to lower reliability of the test statistics and forecast coverage intervals. The results in columns (6) and (7) of Table 5 show that, in our dataset, the null hypothesis of no autocorrelation cannot be rejected, which means the residuals do exhibit a linear structure. Table 5: P-Values of RegARIMA Residual Tests NACE Code Normality Independence Randomness Linearity DoornikHansen LjungBox BoxPierce Runs around mean number Runs around mean length Ljung-Box on squared residuals Box-Pierce on squared residuals (1) (2) (3) (4) (5) (6) (7) A 0.765 0.753 0.903 0.901 1.000 0.893 0.972 B 0.947 0.543 0.753 0.989 1.000 0.623 0.802 C 0.712 0.637 0.894 0.205 1.000 0.616 0.886 D 0.903 0.587 0.824 0.368 1.000 0.047 0.202 E 0.797 0.943 0.989 0.871 1.000 0.365 0.616 F 0.540 0.971 0.993 0.796 1.000 0.061 0.278 G 0.218 0.867 0.964 0.510 1.000 0.767 0.937 H 0.567 0.586 0.820 0.300 1.000 0.469 0.707 I 0.911 0.473 0.743 0.407 1.000 0.581 0.803 J 0.954 0.562 0.821 0.067 0.984 0.680 0.843 K 0.430 0.915 0.985 0.698 1.000 0.737 0.907 L 0.230 0.911 0.959 0.447 1.000 0.966 0.990 M 0.585 0.075 0.307 0.950 1.000 0.824 0.931 N 0.844 0.648 0.884 0.203 1.000 0.455 0.709 Continued on the next page 19 NACE Code Normality Independence Randomness Linearity DoornikHansen LjungBox BoxPierce Runs around mean number Runs around mean length Ljung-Box on squared residuals Box-Pierce on squared residuals (1) (2) (3) (4) (5) (6) (7) O 0.401 0.836 0.935 0.638 1.000 0.003 0.057 P 0.275 0.357 0.621 0.003 0.023 0.792 0.931 Q 0.813 0.442 0.683 0.531 1.000 0.130 0.372 R 0.703 0.091 0.292 0.183 1.000 0.403 0.630 S 0.244 0.600 0.847 0.948 1.000 0.136 0.456 T 0.236 0.348 0.652 0.901 1.000 0.888 0.961 Source: Authors’ calculations. After ensuring all of the critical assumptions are satisfied in the pre-treatment stage, we analyze the quality of the seasonal adjustment results using a set of “M diagnostics” produced by JDemetra+. The various indicators assess different aspects of the seasonal adjustment process, such as how much the irregular component contributes to the overall variance (M1, M2, and M3), the randomness of the irregular component (M4), the significance of changes in the trend and irregular components (M5), the ratio of annual changes in the irregular component to the seasonal component (M6), the presence of identifiable seasonality (M7), and the stability of shortand long-term variations (M8, M9, M10, and M11). In addition, JDemetra+ produces two composite indicators (Q and Q − M2), which assess the overall quality of the models. Values exceeding 1 suggest possible problems with the adjustment, while values ranging from 0 to 1 are considered satisfactory. The M-diagnostic indicators for all sectors, presented in Table 6, suggest the seasonal adjustment process is generally satisfactory for most sectors. However, a few sectors exhibit potential issues in specific indicators. In particular, some sectors, like mining and quarrying (B), manufacturing (C), and information and communication (J), have problems with moving seasonality, as indicated by M10 and M11 statistics exceeding the acceptable value of 1. Similarly, several sectors have a high irregular component, such as real estate activities (L), administrative and support service activities (N), and other service activities (S). However, for all sectors, the two composite indicators have values less than 1, confirming that, overall, the seasonal adjustment process appears to be adequate. 20 Table 6: The M-Diagnostics NACE Code M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 Q Q-M2 A 0.0 0.0 1.3 1.2 1.0 1.2 0.1 0.3 0.2 0.3 0.3 0.5 0.5 B 0.6 0.1 0.2 0.5 0.2 0.3 0.6 1.0 0.7 1.5 1.4 0.5 0.6 C 0.1 0.1 0.5 0.2 0.7 0.9 0.3 0.8 0.6 1.5 1.5 0.5 0.5 D 0.7 0.4 1.3 0.6 1.3 0.8 0.4 1.4 0.8 1.6 1.6 0.9 0.9 E 0.8 0.1 0.6 0.5 0.5 0.5 0.4 0.8 0.5 0.8 0.7 0.5 0.6 F 0.0 0.0 0.3 0.6 0.6 1.1 0.1 0.3 0.2 0.5 0.4 0.3 0.3 G 0.0 0.0 0.0 0.3 0.2 1.0 0.3 0.5 0.5 0.4 0.4 0.2 0.3 H 0.8 0.3 0.4 0.9 0.4 0.9 0.2 0.2 0.1 0.2 0.2 0.4 0.4 I 0.1 0.0 0.0 0.2 0.2 0.7 0.3 0.7 0.1 0.6 0.4 0.2 0.2 J 1.1 0.2 0.3 0.7 0.2 0.1 0.4 1.1 0.9 1.2 1.2 0.6 0.6 K 0.1 3.0 0.0 0.7 0.2 0.3 0.4 1.1 0.4 0.9 0.7 0.7 0.4 L 1.2 0.9 1.0 0.5 1.0 0.5 0.5 1.2 0.9 1.6 1.5 0.9 0.9 M 0.3 0.3 0.9 0.3 0.7 0.3 0.3 0.6 0.3 0.9 0.9 0.5 0.5 N 0.7 1.1 1.2 1.0 1.0 0.1 0.3 0.6 0.2 0.7 0.7 0.7 0.6 O 0.7 0.8 1.8 0.3 1.5 0.1 0.4 0.8 0.7 0.4 0.4 0.7 0.7 P 0.1 0.1 1.1 1.2 0.9 0.3 0.2 0.4 0.3 0.4 0.4 0.5 0.5 Q 0.3 0.2 0.8 0.6 0.9 0.5 0.3 0.9 0.6 0.7 0.7 0.6 0.6 R 0.2 0.0 0.0 0.7 0.2 0.9 1.0 2.1 0.5 2.1 2.0 0.7 0.8 S 1.2 0.5 1.0 0.7 0.9 0.1 0.4 0.9 0.3 0.8 0.4 0.7 0.7 T 0.1 0.1 0.9 0.2 0.8 0.3 0.1 0.4 0.3 0.7 0.7 0.4 0.4 Source: Authors’ calculations. Seasonally adjusted time series should remain consistent, showing minimal variation when a few observations are added or removed from the original data. To evaluate this stability, we use sliding spans analysis, which examines how seasonal adjustment results fluctuate when different portions of the original dataset are used. This method specifically assesses the estimated seasonal factors and the quarter-to-quarter changes in the seasonally adjusted series, providing warnings if there is too much variability for the same quarter or if the count of unstable seasonal factors or changes surpasses acceptable thresholds. In JDemetra+, a threshold of 3% of the test statistics is used to identify abnormal values. Following IMF guidelines, seasonal adjustment results are deemed stable when unstable seasonal factors account for less than 15% of all observations, and when abnormal quarter-toquarter variations in the seasonally adjusted series represent less than 35% of the total observations. 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The paper discusses best practices for seasonal adjustment and strategies for accurate real-time economic analysis. About the Asian Development Bank ADB is a leading multilateral development bank supporting inclusive, resilient, and sustainable growth across Asia and the Pacific. Working with its members and partners to solve complex challenges together, ADB harnesses innovative financial tools and strategic partnerships to transform lives, build quality infrastructure, and safeguard our planet. Founded in 1966, ADB is owned by 69 members—50 from the region. FROM NOISE TO TURNING POINTS A NEW FRAMEWORK FOR SEASONAL ADJUSTMENT IN ARMENIA Gevorg Minasyan, Stefan Schipper, Lusya Khachatryan, Seda Movsisyan, and Pamela Lapitan From the People of Japan JFPR Japan Fund for Prosperous and Resilient Asia and the Pacific