Seasonal Adjustment

The effects of seasonally adjusted 24-h exposure to cold and darkness on cognitive performance in urban circumpolar residents was assessed in 15 male subjects who spent three 24-h periods in a climatic chamber at 65 ° latitude during the winter (January-March) and/or summer (August-September). Each subject was exposed to three different environmental conditions in random order: (1) 22 ° C temperature and 500 lx lighting; (2) 10 ° C temperature and 500 lx lighting; and (3) 10 ° C temperature and 0.5-l lx lighting. Accuracy on an addition-subtraction task was significantly greater in the summer than in the winter (p = 0.038), while accuracy on a repeated acquisition task was significantly greater in the winter than in the summer (p < 0.001). Independent of season, exposure to cold and darkness was significantly associated with a decline in response time on five cognitive tests, an improvement in accuracy on three tests measuring complex cognitive tasks, and a decline in accuracy on two tests measuring simple tasks. Increased performance on complex tasks may result from increased arousal in response to the combination of cold temperatures and dim light characteristic of the winter in urban circumpolar settings.

We test for the presence of low-dimensional chaotic structure in crude oil, heating oil, and unleaded gasoline futures prices from the early 1980s. Evidence on chaos will have important implications for regulators and short-term trading strategies. While we find strong evidence of non-linear dependencies, the evidence is not consistent with chaos. Our test results indicate that ARCH-type processes, with controls for seasonal variation in prices, generally explain the non-linearities in the data. We also demonstrate that employing seasonally adjusted price series contributes to obtaining robust results via the existing tests for chaotic structure. Maximum likelihood methodologies, that are robust to the non-linear dynamics, lend support for Samuelson's hypothesis on contract-maturity effects in futures price-changes. However, the tests for chaos are not found to be sensitive to the maturity effects in the futures contracts. The results are robust to controls for the oil shocks of 1986 and 1991. ᮊ A. Chatrath . 0140-9883r01r$ -see front matter ᮊ 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S 0 1 4 0 -9 8 8 3 0 0 0 0 0 7 9 -7 ( )

Considering the unique seasonal pattern in university dining environments, this study attempts to determine the degree of improvement in accuracy of each forecasting method tested when season-alIy adjusted data is employed. This study also seeks to identify the most accurate forecasting method of the six forecasting methods used in this study: naIve, moving average, simple exponential smoothing, Holt's method, Winter's method, and linear regression. Accuracy is measured using Mean Squared Error, Mean Absolute Percentage Error, and Mean Percentage Error. Results show that Winter's method outperforms the other tive methods when raw data is used, while Moving Average method, when used with seasonally adjusted data, is the most accurate

We conduct tests for the presence of low-dimensional chaotic structure in the futures prices of four important agricultural commodities. Though there is strong evidence of non-linear dependence, the evidence suggests that there is no long-lasting chaotic structure. The dimension estimates for the commodity futures series are generally much higher than would be for low dimension chaotic series. Our test results indicate that autoregressive conditional heteroskedasticity (ARCH)-type processes, with controls for seasonality and contract-maturity effects, explain much of the non-linearity in the data. We make a case that employing seasonally adjusted price series is important in obtaining robust results via some of the existing tests for chaotic structure. Finally, maximum likelihood methodologies, that are robust to the non-linear dynamics, lend strong support to the Samuelson hypothesis of maturity effects in futures price changes.

Many economic time series exhibit important systematic fluctuations within the year, i.e. seasonality. Differently from usual practice, we argue that using original data should always be considered, although their process is more complicated than that of seasonally adjusted data. Motivations to use not adjusted data come from the information contained in their peak and trough and from economic theory. One major complication is instead the unit root at seasonal frequencies. In this paper we tackle the issue implementing a test to identify the source of seasonality. In particular we follow for quarterly data.

As might be expected, surveys show accuracy is the most important criterion in selecting a forecasting strategy. This may lead to the expectation that computer based software would be used to aid the forecasting eort. However, despite the wide availability of forecast software, management judgement appears to be the preferred method. This leads to the question: does management judgement provide the most accurate forecast estimates? This paper reports a ®eld study of judgemental sales forecasting over thirteen manufacturing organisations to investigate whether these forecasts are accurate, unbiased and ecient, and whether better ex ante forecasts could have been developed using a computer based model. The study shows that the company forecasts were not uniformly more accurate than a simple, un-seasonally adjusted, na õve forecast. Most of the source of error is due to both ineciency (a serial correlation in the errors) and bias in the forecasts. These two factors seemed to mask any contribution of contextual information to accuracy. The results are also discussed in terms of forecasting objectives the organisations may have other than accuracy.

The dates of holidays such as Eid-ul Fitr, Eid-ul Adha, Chinese New Year and Deepavali vary from one year to the next and non-fixed date can affect time series data. The moving holidays need to be taken into consideration in the seasonal adjustment process to avoid misleading interpretations on the seasonally adjusted and trend estimates. Hence, by removing the moving holiday effect, the important features of economic series, such as the turning points can be easily identified. Seasonally adjusted data also allows meaningful comparisons to be made over a shorter time frame and it also reflects real economic movements. Currently, there are various methods applied for seasonal adjustment such as the X-12 ARIMA. However, these methods can only be used to adjust for the North American Easter effect and there is no such method which can deal with holiday effects in Malaysia such as Eid-ul Fitr, Eid-ul Adha, Chinese New Year and Deepavali. Due to these limitations, this paper proposes a procedure for seasonal adjustment of moving holiday effects in Malaysian economic time series data called SEAM (Seasonal Adjustment for Malaysia). The procedure involves estimating the irregular components using the X-12 ARIMA program and subsequently removing the moving holiday effects using a regression method. Three types of regressors namely, REG1 (using one weight variable), REG2 (using two weight variables) and REG3 (using three weight variables) are proposed in this study to measure the Eid-ul Fitr, Chinese New Year and Deepavali effects. Overall, it is found that SEAM is an effective method in removing the Malaysian moving holiday effects.

This paper investigates the performance of various conditional volatility models to forecast the second moment of tanker freight rates. Justified by existing theoretical and empirical evidence, we focus on asymmetric Markov regime-switching models to study the major global routes for long-haul trade of crude oil during the sample period from June 2000 to May 2015. Moreover, in contrast to a number of existing studies, we examine seasonally adjusted freight rates. We find that regime-switching GARCH models outperform their single-regime complements in terms of in-sample fit and out-of-sample forecasting accuracy. In particular, the asymmetric MRS-EGARCH and MRS-APARCH exhibit superior in- and out-of-sample performance. To additionally examine the applicability in freight risk management, we compare Value-at-Risk and Expected Shortfall forecasts. Our results show that accounting for volatility regimes and asymmetry does not enhance the performance of one-day-ahead forecasts of either risk measure for both long and short trading positions.

This paper applies methods of seasonal ARIMA time series analysis to U. S. monthly birth and death rates for January 1950-December 1978. For model selection, the conventional Box-Jenkins (1970, 1976) diagnostic checks are used in conjunction with some suggestions of Nerlove et al. (1979). This results in final models that contain significant second-order autoregressive components, as well as seasonal moving-average components, for both series. In addition, some evidence is found in the birth rate series for weekly periodicities. These findings imply the existence of a seasonal adjustment procedure that improves on the Census X-II program currently used by vital statistics agencies.

Due to their high relative cost, solar electric energy systems have yet to be exploited on a widespread basis. It is believed in the energy community that a technology similar to photovoltaic (PV), but offered at about $1/W would lead to widespread deployment at residential and commercial sites. This paper addresses the investigation and feasibility study of a low-cost solar thermal electricity generation technology, suitable for distributed deployment. Specifically, we discuss a system based on nonimaging solar concentrators, integrated with free-piston Stirling engine devices incorporating integrated electric generation. We target concentratorcollector operation at moderate temperatures, in the range of 125 • C to 150 • C. This temperature is consistent with use of optical concentrators with concentration ratios on the order of 1-2. These low ratio concentrators admit wide angles of radiation acceptance and are thus compatible with no diurnal tracking, and no or only a few seasonal adjustments. Thus, costs and reliability hazards associated with tracking hardware systems are avoided. Further, we note that in the intended application, there is no shortage of incident solar energy, but rather it is the capital cost of the solar-electric system that is most precious. Thus, we outline a strategy for exploiting solar resources in a cost constrained manner. The paper outlines design issues, and a specific design for an appropriately dimensioned free-piston Stirling engine. Only standard low-cost materials and manufacturing methods are required to realize such a machine.

This paper focuses on the construction of a composite leading indicator (CLI) for Turkish economic activity to provide earlier signals of turning points between expansions and slowdowns. For this analysis, Index of Industrial Production (IIP) is used as an indicator of economic activity and a broad set of economic indicators related with IIP are analyzed to find leading indicators that perform well both in forecasting and tracking cyclical developments of the economic activity. From the broad set of series, seven of them are selected as leading indicators. The selected indicators constitute a balanced subset of demand, supply and policy variables. While constructing CLI, growth cycle approach is used and the cyclical pattern of the series are obtained by eliminating seasonal, irregular and trend components via TRAMO/SEATS and HP filter. Selected leading indicators are combined into a composite leading indicator using the optimal weights derived from principal component analysis. It is found that CLI is anticipating the IIP and it performed well both in tracking and predicting previous turning points of IIP. JEL Classification: E32, C19

Different estimates of the seasonal effects in an economic time series can arise from different choices of the options in the seasonal adjustment software. Or, with an aggregate series, different estimates can also result from different choices of the level of aggregation at which seasonal adjustment is performed. One purpose of this paper is to illustrate some issues that arise in the seasonal adjustment of aggregate series. A second focus is to describe some useful ways of detecting adjustment inadequacies and assessing the quality of the adjustments.

A general methodology is described for identifying and statistically modeling trends which may be contained in a water quality time series. A range of useful exploratory data analysis tools are suggested for discovering important patterns and statistical characteristics of the data such as trends caused by external interventions. To estimate the entries in an evenly spaced time series when data are available at irregular time intervals, a new procedure based upon seasonal adjustment is described. Intervention analysis is employed at the confirmatory data analysis stage to rigorously model changes in the mean levels of a series which are identified using exploratory data analysis techniques. Furthermore, intervention analysis can be utilized for estimating missing observations when they are not too numerous. The effects of cutting down a forest upon various water quality variables and also the consequences of acid rain upon the alkalinity in a stream provide illustrative applications which demonstrate the effectiveness of the methodology.

This paper examines the information available through leading indicators for modelling and forecasting the UK quarterly index of production. Both linear and non-linear specifications are examined, with the latter being of the Markov-switching type as used in many recent business cycle applications. The Markov-switching models perform relatively poorly in forecasting the 1990s production recession, but a three indicator linear specification does well. The leading indicator variables in this latter model include a short-term interest rate, the stock market dividend yield and the optimism balance from the quarterly CBI survey.

The aim of this study was to assess the accuracy of different methods of forecasting malaria incidence from historical morbidity patterns in areas with unstable transmission. We tested five methods using incidence data reported from health facilities in 20 areas in central and north-western Ethiopia. The accuracy of each method was determined by calculating errors resulting from the difference between observed incidence and corresponding forecasts obtained for prediction intervals of up to 12 months. Simple seasonal adjustment methods outperformed a statistically more advanced autoregressive integrated moving average method. In particular, a seasonal adjustment method that uses mean deviation of the last three observations from expected seasonal values consistently produced the best forecasts. Using 3 years' observation to generate forecasts with this method gave lower errors than shorter or longer periods. Incidence during the rainy months of June-August was the most predictable with this method. Forecasts for the normally dry months, particularly December-February, were less accurate. The study shows the limitations of forecasting incidence from historical morbidity patterns alone, and indicates the need for improved epidemic early warning by incorporating external predictors such as meteorological factors.

In this paper, forecasting models for the monthly outgoing telephone calls in a University Campus are presented. The data have been separated in the categories of international and national calls as well as calls to mobile phones. The total number of calls has also been analyzed. Three different methods, namely the Seasonal Decomposition, Exponential Smoothing Method and SARIMA Method, have been used. Forecasts with 95% confidence intervals were calculated for each method and compared with the actual data. The outcome of this work can be used to predict future demands for the telecommunications network of the University. D

Several important economic time series are recorded on a particular day every week. Seasonal adjustment of such series is difficult because the number of weeks varies between 52 and 53 and the position of the recording day changes from year to year. In addition certain festivals, most notably Easter, take place at different times according to the year. This article presents a solution to problems of this kind by setting up a structural time series model that allows the seasonal pattern to evolve over time and enables trend extraction and seasonal adjustment to be carried out by means of state-space filtering and smoothing algorithms. The method is illustrated with a Bank of England series on the money supply.

How much effort to expend in any one bout of reproduction is among the most important decisions made by an individual that breeds more than once. According to life-history theory, reproduction is costly, and individuals that invest too much in a given reproductive bout pay with reduced reproductive output in the future. Likewise, investing too little does not maximize reproductive potential. Because reproductive effort relative to output can vary with predictable and unpredictable challenges and opportunities, no single level of reproductive effort maximizes fitness. This leads to the prediction that individuals possessing behavioural mechanisms to buffer challenges and take advantage of opportunities would incur fitness benefits. Here, we review evidence in birds, primarily of altricial species, for the presence of at least two such mechanisms and evidence for and against the seasonal coordination of these mechanisms through seasonal changes in plasma concentrations of the pituitary hormone prolactin. First, the seasonal decline in clutch size of most bird species may partially offset a predictable seasonal decline in the reproductive value of offspring. Second, establishing a developmental sibling-hierarchy among offspring may hedge against unpredictable changes in resource availability and offspring viability or quality, and minimize energy expenditure in raising a brood. The hierarchy may be a product, in part, of the timing of incubation onset relative to clutch completion and the rate of yolk androgen deposition during the laying cycle. Because clutch size should influence the effects of both these traits on the developmental hierarchy, we predicted and describe evidence in some species that females adjust the timing of incubation onset and rate of yolk androgen deposition to match clutch size. Studies on domesticated precocial species reveal an inhibitory effect of the pituitary hormone prolactin on egg laying, suggesting a possible hormonal basis for the regulation of clutch size. Studies on the American kestrel (Falco sparverius) and other species suggest that the seasonal increase in plasma concentrations of prolactin may regulate both a seasonal advance in the timing of incubation onset and a seasonal increase in the rate of yolk androgen deposition. These observations, together with strong conceptual arguments published previously, raise the possibility that a single hormone, prolactin, functions as the basis of a common mechanism for the seasonal adjustment of reproductive effort. However, a role for prolactin in regulating clutch size in any species is not firmly established, and evidence from some species indicates that clutch size may not be coupled to the timing of incubation onset and rate of yolk androgen deposition. A dissociation between the regulation of clutch size and the regulation of incubation onset and yolk androgen deposition may enable an independent response to the predictable and unpredictable challenges and opportunities faced during reproduction.

The hypothesis is advanced that the circadian pacemaker in the mammalian suprachiasmatic nucleus (SCN) is composed at the molecular level of a nonredundant double complex of circadian genes (per1, cry1, and per2, cry2). Each one of these sets would be sufficient for the maintenance of endogenous rhythmicity and thus constitute an oscillator. Each would have slightly different temporal dynamics and light responses. The per1/cry1 oscillator is accelerated by light and decelerated by darkness and thereby tracks dawn when day length changes. The per2/cry2 oscillator is decelerated by light and accelerated by darkness and thereby tracks dusk. These M (morning) and E (evening) oscillators would give rise to the SCN's neuronal activity in an M and an E component. Suppression of behavioral activity by SCN activity in nocturnal mammals would give rise to adaptive tuning of the endogenous behavioral program to day length. The proposition-which is a specification of Pittendrigh and Daan's E-M oscillator model-yields specific nonintuitive predictions amenable to experimental testing in animals with mutations of circadian genes.

This study empirically investigates the role of trade policy along with physical capital, human capital and labour force on economic growth in an isolated economy (ie North Cyprus). We use a sample of quarterly and seasonally adjusted data covering the period 1978Q1-2002Q4 ...

In this chapter we use a simulation experiment to examine whether theseasonal adjustment methods Census X12-ARIMA and TRAMO/SEATS effectivelyremove seasonality properties from time series data, while preserving otherfeatures like the stochastic trend. As data generating processes we use avariety of processes that are actually found in practice. These processesinclude constant seasonality, changing seasonal patterns due to seasonalunit roots and processes

Focusing on the widely-used Box-Jenkins "airline" model, we show how the class of seasonal ARIMA models with a seasonal moving average factor can be parsimoniously generalized to model time series with heteroskedastic seasonal frequency components. Our frequency-specific models decompose this factor by associating one moving average coefficient with a proper subset of the seasonal frequencies 1, 2, 3, 4, 5 and 6 cycles per year and a second coefficient with the complementary subset. A generalization of Akaike's AIC is presented to determine these subsets. Properties of seasonal adjustment filters and adjustments obtained from the new models are examined as are forecasts.

Using software being developed by the National Bank of Belgium to estimate and select among Frequency Specific Models, we investigate how often these models are selected over the Box-Jenkins Airline model, which they generalize, for a set of BLS series and a set of Census Bureau series. Consequences for seasonal adjustment are considered, as is the stability under future data additions of the model selection procedure used to select among these models.

In addition to seasonal changes in reproductive function, seasonal changes in immune function are mediated by the pineal hormone, melatonin. Melatonin affects immune function both indirectly, acting through other hormones, and directly by acting on components of the immune system. Melatonin also affects tumorigenesis and tumor development. We hypothesize that many of the indirect effects of melatonin on immune function are mediated through glucocorticoids, and appear to be part of an integrated series of adaptations to manage energy. Direct effects of melatonin on immune function appear to be mediated by melatonin receptors on lymphatic tissue or on immune cells in circulation. Winter is energetically demanding and stressful; thermoregulatory demands typically increase when food availability decreases. Individuals would enjoy a survival advantage if seasonally recurring stressors could be anticipated and countered by bolstering immune function. To summarize, melatonin may be part of...

9 2 The Unrestricted VAR and its components 11 2.1 Introduetion 11 2.2 The model 12 2.3 Univariate processes and unit roots 15 2.4 Integrated processes 18 2.4.1 Definitions and notation 18 2.4.2 MA representation, autocorrelation and pseudo spectrum 2.5 Alternative models for nonstationarity, long memory and persistenee 2.5.1 Nonstationarity 2.5.2 Long memory, the varianee time function and adjusted range analysis 2.5.3 Persistenee Appendix A2.1 MA representation integrated process A2.1.1 MA representations A2.

In this paper we focus on two 'STS' models suitable for forecasting the index of industrial production. The first model requires that the index be transformed with a first and seasonal difference filters. The second model considers the index in its second difference filter, while seasonality is modeled with a constant and seasonal dummy variables. Tests designed to discriminate empirically between these two models are also conducted. Our results prefer the performance of the second model, particularly when the conventional ML estimation procedure is replaced by the ALS procedure. This process together with appropriate seasonal adjustment advances the possibility of using the suggested index forecasts to help to predict business cycle turning points.

Biological data from 66 populations of Arctic charr, Salvelinus alpinus, from eastern North America were analysed to test the applicability of the countergradient hypothesis as an explanation of differences in seasonally adjusted growth rates. Samples were obtained along a 37°latitudinal gradient and partitioned among anadromous, normal lacustrine, and dwarf lacustrine Arctic charr morphotypes. Models relating length-at-age or age-specific growth rates to latitude were estimated for each morphotype. Lengthat-age declined with latitude for anadromous and lacustrine charr. Age-specific growth rates also varied with latitude, particularly for normal lacustrine charr. Results of analyses provide support for the countergradient hypothesis in growth performance of normal lacustrine morphotypes, where northern populations compensate for the shorter growth season with a greater rate of growth than southern populations. Anadromous charr exhibited equivocal evidence of countergradient variation, while results for dwarf lacustrine Arctic charr populations were inconclusive owing to the limited range of ages, and latitudes for which data were available.

The hypothesis is advanced that the circadian pacemaker in the mammalian suprachiasmatic nucleus (SCN) is composed at the molecular level of a nonredundant double complex of circadian genes ( per1, cry1, and per2, cry2). Each one of these sets would be sufficient for the maintenance of endogenous rhythmicity and thus constitute an oscillator. Each would have slightly different temporal dynamics and light responses. The per1/ cry1 oscillator is accelerated by light and decelerated by darkness and thereby tracks dawn when day length changes. The per2/ cry2 oscillator is decelerated by light and accelerated by darkness and thereby tracks dusk. These M (morning) and E (evening) oscillators would give rise to the SCN&#39;s neuronal activity in an M and an E component. Suppression of behavioral activity by SCN activity in nocturnal mammals would give rise to adaptive tuning of the endogenous behavioral program to day length. The proposition—which is a specification of Pittendrigh and Daan...

This paper applies the programs TRAMO ("Time Series Regression with ARIMA Noise, Missing Observations and Outliers " ) and SEATS (" Signal Extraction in ARIMA Time Series" ) to seasonal adjustment of the monthly Consumer Price Index Swiss series. It is shown how the results of the purely automatic procedure can be improved with two simple modifications: one that emerges from the TRAMO-SEATS diagnostics, and another that uses "a-priori" information. In particular, the SEATS output is used to select a model among the ones that are equally compatible with the sample. Identification and estimation is done for data finishing in May 1999, and 10 additional observations are used to illustrate the out-of-sample performance of the TRAMO-SEATS procedure.

In India, year-on-year percentage changes of price indexes are widely used as the measure of inflation. In terms of monthly data, each observation of a one-year change in inflation is the sum of twelve onemonth changes. This suggests that better information about inflationary pressures can be obtained using point-on-point monthly changes. This requires seasonal adjustment. We apply standard seasonal adjustment procedures in order to obtain a point-on-point seasonally adjusted monthly time-series of inflation in India. In three interesting high inflation episodes -1994-95, 2007 and 2008 -we find that this data yields a faster and better understanding of inflationary pressures.

This paper investigates the intraday and day-of-the-week seasonalities, as well as the non-linear dynamics of the two most traded American stock Index futures, i.e. the E-mini SP500 and the E-mini Nasdaq100, quoted on the Chicago Mercantile Exchange. The dataset covers both European and American trading hours. We employ the periodic autoregressive model together with the asymmetric periodic GARCH (PAR -APGARCH), with a flexible distribution given by the Skew-T, which allows for both conditional skewness and kurtosis. Differently from previous approaches, we directly model the strong seasonalities in the behavior of the conditional mean, volatility, skewness and kurtosis, and we avoid to use the common seasonal adjustment procedures, which can generate misleading inferences and blur the characteristics of the data (see Franses 1996, Osborn 2004).

In July 2003, a house with a seasonally adjusted annual average radon concentration of 49 000 Bq m −3 was identified near Castleisland in County Kerry (SW Ireland). The possibility that other houses with similar extreme radon concentrations could be present in the surrounding area triggered the setting up of a localised radon survey, the so-called 'Castleisland Radon Survey' (CRS). To this end, approximately 2500 householders living in four 10×10 km 2 grid squares from the Irish grid closest to the town of Castleisland were invited to participate. Four hundred and eighteen householders responded to the invitation (17% response rate) and 383 home results were used for further analysis. In the 400 km 2 encompassing the four studied grid squares, 14% of the homes were found to have a seasonally adjusted annual average radon concentration above the national reference level of 200 Bq m −3 while 2% above 800 Bq m −3 . An average radon concentration of 147 Bq m −3 was calculated. This can be compared with the average radon concentration of 98 Bq m −3 calculated for the same four grid squares on the basis of 80 measurements carried out during the Irish National Radon Survey (NRS) which was conducted between 1992 and 1997. The fourth highest radon concentration (6184 Bq m −3 ) and three of the ten highest ever measured in Ireland were all identified during the CRS. This shows that localised and targeted radon surveys are an invaluable tool for the identification of homes at highest risk from high radon concentrations. Two of the four grid squares investigated during the CRS are currently designated as high radon areas (defined as areas where 10% or more of all houses are predicted to exceed 200 Bq m −3 ) as predicted by the NRS. A thorough statistical analysis of the CRS and NRS data was carried

We present two types of diagnostics for SEATS and similar programs. We start with modi…cations of the diagnostic used by SEATS to detect underestimation or overestimation, meaning inadequate or excessive supression of frequency components near the target frequen- cies, e.g. the seasonal frequencies in the case of seasonal adjustment. The modi…cations use time-varying variances of the …nite-length …lter output instead

Among the alternative Unobserved Components formulations within the stochastic state space setting, the Dynamic Harmonic Regression (DHR) has proved particularly useful for adaptive seasonal adjustment signal extraction, forecasting and back-casting of time series. Here, we show first how to obtain ARMA representations for the Dynamic Harmonic Regression (DHR) components under several random walk specifications. Later, we uses these theoretical results to derive an alternative algorithm based on the frequency domain for the identification and estimation of DHR models. The main advantages of this algorithm are linearity, fast computing, avoidance of some numerical issues, and automatic identification of the DHR model. To compare it with other alternatives, empirical applications are provided.

Downloadable! This paper was written as a technical note to explain the seasonal adjustment procedure used by the Central Bank of Chile. The methodology used here, named X-12-ARIMA, was developed by the US Census Bureau. This paper also includes a procedure manual ...