Seasonal Adjustment Procedures Research Articles

Outlier identification and adjustment for time series

Identification and replacement of erroneous data is of fundamental importance for the quality of statistical surveys. If statistical units are continuously sampled over an extended period, time series methods can facilitate this task. Numerous outlier identification and replacement procedures are accessible for this particular purpose, like RegArima Approaches within the seasonal adjustment procedures in X13-Arima or Tramo/Seats. These algorithms can be used to identify different types of outliers, like additive outliers, level shifts or transitory changes. In this paper an alternative outlier identification procedure is proposed which is based on a nonlinear model estimated with support vector regressions. The focus of this procedure is on the identification of additive outliers and on the applicability for short time series with less than 3 years of observations.

Monitoring the direction of the short-term trend of economic indicators

Socioeconomic indicators have long been used by official statistical agencies to analyze and assess the current stage at which the economy stands via the application of linear filters used in conjunction with seasonal adjustment procedures. In this study, we propose a new set of symmetric and asymmetric weights that offer substantial gains in real-time by providing timely and more accurate information for detecting short-term trends with respect to filters commonly applied by statistical agencies. We compare the new filters to the classical ones through application to indicators of the US economy, which remains the linchpin of the global economic system. To assess the superiority of the proposed filters, we develop and evaluate explicit tests of the null hypothesis of no difference in revision accuracy of two competing filters. Furthermore, asymptotic and exact finite-sample tests are proposed and illustrated to assess if two compared filters have equal probabilities of failing to detect turning points at different time horizons after their occurrence.

COVID-19 and Seasonal Adjustment

In this paper we study the impact of COVID-19 on seasonal adjustment. We focus on whether special adjustments are required to treat the COVID-19 crisis as an outlier as suggested by Eurostat in the application of three seasonal adjustment procedures: X13-ARIMA-SEATS, the industry standard, Seasonal-Trend decomposition based on Loess (STL) and a new method CAMPLET, a acronym of its tuning parameters. In addition we investigate whether revisions occur. We show results of seasonal adjustments for the quarterly series real GDP in the Netherlands, and the weekly series U.S. Initial Claims. Seasonal adjustment with X13-ARIMA-SEATS and CAMPLET requires modifications in the implementation of the standard procedure to treat the COVID-19 crisis as an outlier; STL can be applied straightforwardly. Differences in seasonally adjusted values are generally small around COVID-19. Finally, X13-ARIMA-SEATS and STL seasonal adjustments are subject to revision, which probably will lead to the COVID-19 crisis becoming less deep when new observations become available.

An improved definition of official excess winter mortality statistics as the basis for detailed analysis and monitoring

In official statistics, excess winter mortality, the number of additional deaths in a winter period, is typically defined as the difference between mortality in a winter period relative to the nonwinter periods before and after. We note two limitations of this approach: (1) the data for the period after winter is available only later, so estimates of excess winter mortality are not timely; (2) unusually high or low numbers of deaths in the non-winter periods can affect estimates. We propose an alternative statistic based on the application of standard seasonal adjustment procedures. We compare the approaches and present some illustrative analyses. The new statistic provides a more objective and timely official series, but is susceptible to revisions, which are shown to be small in practice. We recommend it as the basis of more detailed monitoring and modelling.

Recovering cointegration via wavelets in the presence of non-linear patterns

Abstract Johansen’s Cointegration Test (JCT) performs remarkably well in finding stable bivariate cointegration relationships. Nonetheless, the JCT is not necessarily designed to detect such relationships in presence of non-linear patterns such as structural breaks or cycles that fall in the low frequency portion of the spectrum. Seasonal adjustment procedures might not detect such non-linear patterns, and thus, we expose the difficulty in identifying cointegrating relations under the traditional use of JCT. Within several Monte Carlo experiments, we show that wavelets can empower more the JCT framework than the traditional seasonal adjustment methodologies, allowing for identification of hidden cointegrating relationships. Moreover, we confirm these results using seasonally adjusted time series as US consumption and income, gross national product (GNP) and money supply M1 and GNP and M2.

Optimal Reconciliation of Seasonally Adjusted Disaggregates Taking Into Account the Difference Between Direct and Indirect Adjustment of the Aggregate

Abstract This article presents a new method to reconcile direct and indirect deseasonalized economic time series. The proposed technique uses a Combining Rule to merge, in an optimal manner, the directly deseasonalized aggregated series with its indirectly deseasonalized counterpart. The lastmentioned series is obtained by aggregating the seasonally adjusted disaggregates that compose the aggregated series. This procedure leads to adjusted disaggregates that verify Denton’s movement preservation principle relative to the originally deseasonalized disaggregates. First, we use as preliminary estimates the directly deseasonalized economic time series obtained with the X-13ARIMA-SEATS program applied to all the disaggregation levels. Second, we contemporaneously reconcile the aforementioned seasonally adjusted disaggregates with its seasonally adjusted aggregate, using Vector Autoregressive models. Then, we evaluate the finite sample performance of our solution via a Monte Carlo experiment that considers six Data Generating Processes that may occur in practice, when users apply seasonal adjustment techniques. Finally, we present an empirical application to the Mexican Global Economic Indicator and its components. The results allow us to conclude that the suggested technique is appropriate to indirectly deseasonalize economic time series, mainly because we impose the movement preservation condition to the preliminary estimates produced by a reliable seasonal adjustment procedure.

Reconciliation of seasonally adjusted data with applications to the Swedish quarterly national accounts

Because of the nonlinearity of the seasonal adjustment procedure, the equality between an aggregate series and the sum of its components usually breaks down after seasonally adjusting the series separately. However, some users of official statistics still request consistency between the seasonally adjusted aggregate series and the sum of the corresponding subseries. To achieve the aggregation consistency, a general Denton‐type reconciliation procedure is proposed here. The additivity constraint is imposed on seasonally adjusted components balancing between magnitude and volatility of each series. Some evaluation criteria, based on a set of chosen minimization functions, are further discussed. The implementation and choice of approaches are discussed through a real example by reconciliation of time series in constant prices from the Swedish quarterly national accounts. Finally, some limitations of the method are outlined and possible future works are proposed.

The Spectral Analysis of Labor Force and Profit of Construction Materials Distribution Companies in Romania Analogue Spectrum of Light in Physics

In physics, spectral studies have been observed and quantified since 1822 when Fourier J. (1822) used them in his analysis of thermal conduction. Further, Balmer (1885), studying the hydrogen atom, noticed the existence of the four lengths waveform which characterize the spectrum of the hydrogen atom. Following the research, it determined the number of 364.6 nm that was identified in each hydrogen spectral line. Therefore, Balmer determined the equation to determine the wavelength of the emission or absorption lines. Three years later, physicist Johannes Rydberg generalized Balmer's equation, thus determining the constant Rydberg. Rutherford's model was later improved and in 1913 was introduced Bohr's model and converts justify empirical results in terms of fundamental physical constants. Subsequently, a significant number of physicists approached the spectral analyzes of electromagnetic radiation (in different fields: ultraviolet, X-rays, infrared) and analyzed their characteristics: frequency, amplitude, spectral density. In the economy, the first papers that dealt with spectral analysis emerged in 1960 and consisted of the analysis of seasonal adjustment procedures for time series at macroeconomic level. Starting from the cross-spectral methods were developed methods such as analysis of the movement in the series, the time-frequency methods, etc. The fluctuating nature of the activities of different sectors of activity involves different oscillations in terms of amplitude and frequency, but also oscillations characterized by a higher or lower propagation period, which determines the evolution of economic indicators. We can classify the propagation periods of activities according to the level of the characteristics that determine them in time units (time intervals). Thus, the oscillation frequency will be given by the number of periods of propagation activities. Depending on the oscillation period will determine their average, and the amplitude of oscillation is determined by peak line and the average determined. Starting from the ultraviolet spectrum in physics and the spectral analyzes made by physicists, analogy we find in the economy elements that refer to the fervent oscillations and form "color strips" and "spectrum". To make "spectral analysis" of such a fluctuating process in terms of frequency and amplitude need a sufficient number of numerical data on the evolution of an economic process.

Robust time series models with trend and seasonal components

We describe observation driven time series models for Student-t and EGB2 conditional distributions in which the signal is a linear function of past values of the score of the conditional distribution. These specifications produce models that are easy to implement and deal with outliers by what amounts to a soft form of trimming in the case of t and a soft form of Winsorizing in the case of EGB2. We show how a model with trend and seasonal components can be used as the basis for a seasonal adjustment procedure. The methods are illustrated with US and Spanish data.

Genetic Algorithm Calibration of Seasonal BVAR Models

In this paper we explore the use of Genetic Algorithms (GA) to calibrate seasonal BVAR models. In this way, the mechanistic use of seasonal adjustment procedures is avoided, since seasonality becomes a structural, basic and explicit part of the BVAR model. At the same time, the use of GA allows calibration to be performed on a diffuse setting, preserving as much as possible the flexible nature of BVAR and revealing interesting features of the data. The well-known U.S. housing data are used to illustrate the procedures outlined in the paper.

The revision policy of seasonally adjusted balance sheet data in Italy

This article illustrates the seasonal adjustment procedure for bank deposits and loans in Italy focusing on the revision policy of seasonally adjusted data. Seasonal adjustment is conducted in a semi-automatic way, employing TRAMO–SEATS, one of the software packages most often used for the production of seasonally adjusted series. Regarding the frequency of data revisions, three alternative methods (current adjustment, concurrent adjustment and partial concurrent adjustment) are tested according to a quantitative criterion. An empirical application allows us to measure the speed of convergence of the estimates obtained with the aforementioned updating methods towards a ‘final’ value that can be considered a benchmark. The results suggest using the method of partial concurrent adjustment, which is based on the identification of the ARIMA model and of the deterministic components once a year, whereas the updating of the corresponding coefficients is undertaken every month.

Variable-ordering induced problems of impulse-response analysis and other difficulties: the dividend policy of Austrian firms

Orthogonalised impulses are the standard way to isolate shocks to variables in a vector error correction model. While using the Cholesky decomposition to adjust interdependencies of the shocks, the ordering of the variables on the stage of estimation has a great impact on the resulting impulse response functions. It is shown how the variable ordering affects the empirical evaluation of the dividend policy of Austrian firms examining corporate earnings, dividends and inflation. Additional problems are discussed (e.g., bootstrapped confidence intervals and seasonal adjustment procedures, missing variables). The paper has two messages: it is a fatal flaw of any economic model to omit important variables. Moreover, it is also of major importance to use appropriate econometric modelling techniques.

Seasonal Adjustment of Bank Deposits and Loans

This paper illustrates the seasonal adjustment procedure for bank deposits and loans, focusing on the policy for the revision of seasonally adjusted data. Seasonal adjustment is semi-automatic when the commonly used software package, TRAMO-SEATS, is used to produce seasonally adjusted series. With reference to the frequency of seasonally adjusted data revisions, three alternative methods (current adjustment, concurrent adjustment, partial concurrent adjustment) are tested according to a quantitative criterion. A simulation study measures the speed of convergence of the estimates, obtained with these three updating methods, to reach a “final estimate to be used as a benchmark. The results favour the use of the partial concurrent adjustment method, that suggests identifying the ARIMA model and the effects of the deterministic components once a year, and updating the corresponding coefficients once a month.

SEASONAL ADJUSTMENT OF SOME FINANCIAL INDICATORS OF PAKISTAN

The paper describes the applied seasonal adjustment procedures used for analysis of the financial time series compiled by SBP. We have applied the X-12-ARIMA method in adjusting five important financial series- currency in circulation, broad money, remittances, exports and imports (from the balance of payments data). Adjusted series were found to be satisfactory, with in the tests and practices followed in X-12-ARIMA.

Seasonal Adjustment of Monetary Aggregates: Implementation of New Procedures

The analysis of seasonality in economics and the development of new seasonal adjustment procedures have been following new directions in the last twenty years. We study this question through the work performed at the Banque de France (Monetary Statistic and Studies Directorate) to compile new seasonally adjusted (SA) data. A brief discussion of the academic literature show the necessity to complement the existing software with empirical rules fixed by the practitioner in order to make all the methodological choices clear, thus avoiding any ambiguity. In the implementation of the new production process, we focus on the revision policy of some keys parameters of the whole process in order to minimize the subsequent revisions in the publication of SA data. We illustrate this new methodology with SA series relating to monetary aggregates, including loans to enterprises and to households, and provide a detailed analysis of the consistency between flows and outstanding amount SA figures, an issue particularly relevant for monetary an financial data.

Detecting multiple mean breaks at unknown points in official time series

In this paper, we propose a computationally effective approach to detect multiple structural breaks in the mean occurring at unknown dates. We present a non-parametric approach that exploits, in the framework of least squares regression trees, the contiguity property of data generating processes in time series data. The proposed approach is applied first to simulated data and then to the Quarterly Gross Domestic Product in New Zealand to assess some of anomalous observations indicated by the seasonal adjustment procedure implemented in X12-ARIMA are actually structural breaks.

The choice of time interval in seasonal adjustment: A heuristic approach

A typical problem of the seasonal adjustment procedures arises when the series to be adjusted is subject to structural breaks. In fact, using the full span of the series can result in a biased estimation of the “true” seasonally adjusted series, with unclear evidence showed by the usual diagnostic tests. In these cases the researcher has to decide where to cut-off the observed series to obtain a homogeneous span; this is generally performed by a simple visual inspection of the graph of the series and/or using a-priori information about the occurrence of the break. In this paper we propose a statistical criterion based on a distance measure between filters, evaluating its performance with Monte Carlo experiments.

On model based seasonal adjustment procedures

In this note the unobserved component approach underlying the software package SEATS is compared with the Beveridge-Nelson type of decomposition for seasonal time series. The main strength of the SEATS approach lies in the appealing model formulation and the careful specification and adjustment of the input series. However, there are some theoretical problems with orthogonal decompositions which may be avoided by using the Beveridge-Nelson approach. The German unemployment series is studied to illustrate the properties of the alternative methods practically.

Time Series Properties of the German Production Index

The production index is an important indicator for assessing the cyclical state of the economy. Unfortunately, the monthly time series is contaminated by many noisy components like seasonal variations, calendar and vacation effects. Only part of those nuisance components are explicitly considered in the seasonal adjustment procedures used by statistical agencies. In this paper, we propose a more flexible specification for the seasonal and working day effects and introduce an indicator for the summer vacations effect. We allow for time-varying parameters and show that the resulting Unobserved Components Model delivers more reliable results for the trend and cycle components of the production index.

Moving Holidays and Seasonal Adjustment: The Case of Turkey

When holiday variation is present so that the dates of certain holidays change from year to year, the relatively automatic seasonal adjustment procedures may fail to extract the seasonal component from a series since the holiday effects are not confined to that component. Turkey, a predominantly Muslim country, constitutes a good example of moving holidays since the official calendar is Gregorian, based on the cycles of the Earth around the sun, while significant Islamic holidays are tied to the Hegirian calendar, based on the lunar cycles. One finds significant deterministic seasonality remains in the conventionally de-seasonalized time series and removing the effects of religious seasonality using a very simple method improves the qualities of the de-seasonalized component.