Víctor M. Guerrero

Temporal Disaggregation of Time Series: An ARIMA-based Approach

Summary Many economic time series are only available in temporally aggregated form. When the analysis requires disaggregated data, the analyst faces the problem of deriving these data in the most reasonable way. In this paper a data-based method is developed which produces an optimal estimator of the disaggregated series. The method requires a preliminary estimate of the series, which is adjusted to fulfil the restrictions imposed by the aggregated data. Empirical selection of the preliminary estimate is discussed and a statistic is developed for testing its adequacy. Some comparisons with other methods, as well as numerical illustrations, are presented.

Linear combination of restrictions and forecasts in time series analysis

An important tool in time series analysis is that of combining information in an optimal way. Here we establish a basic combining rule of linear predictors and show that such problems as forecast updating, missing value estimation, restricted forecasting with binding constraints, analysis of outliers and temporal disaggregation can be viewed as problems of optimal linear combination of restrictions and forecasts. A compatibility test statistic is also provided as a companion tool to check that the linear restrictions are compatible with the forecasts generated from the historical data. Copyright

A recursive ARIMA-based procedure for disaggregating a time series variable using concurrent data

SummaryA recursive procedure for temporally disaggregating a time series is proposed. In practice, it is superior to standard non-recursive procedures in several ways: (i) previously disaggregated data need not be modified, (ii) calculations become simpler and (iii) data storage requirements are minimized. The suggested procedure yields Best Linear Unbiased Estimates, given the historical record of previously disaggregated figures, concurrent data in the form of a preliminary series and an aggregated value for the current period. A test statistic is derived for validating the numerical results obtained in practice.

Combining multiple time series predictors: a useful inferential procedure

We present a general result that allows us to combine data from two different sources of information in order to improve the efficiency of predictors within the context of multiple time series analysis. Such a result is derived from generalized least squares and is given as a combining rule that takes into account the possibility of correlation between forecasts and bias in one of them. We then specialize that result to situations in which the predictors are unbiased and uncorrelated. Afterwards we propose measuring precision shares and testing for compatibility in order for the combination to make sense. Several applications of the combining rule are presented according to the nature of the linear constraints imposed by one of the data sources. When the constraints are binding we consider the case of restricted forecasts with exact linear restrictions, deterministic changes in the model structure and partial information on some variables. When the constraints are stochastic we study forecast combinations that include expert judgments and benchmarking. Thus, the connections among different standard techniques are emphasized by the combining rule and its companion compatibility test. An empirical example illustrates the usefulness of this inferential procedure in practice.

Temporal and contemporaneous disaggregation of multiple economic time series

A method is proposed for estimating unobserved values of multiple time series whose temporal and contemporaneous aggregates are known. The resulting estimates are obtained from a model-based procedure in which the models employed are indicated by the data alone. This procedure is empirically supported by a discrepancy measure here derived. Even though the problem can be cast into a state-space formulation, the usual assumptions underlying Kalman filtering are not fulfilled and such an approach cannot be applied directly. Some simulated examples are provided to validate the method numerically and an application with real data serves to illustrate its use in practice.

A Statistical Approach to Provide Individualized Privacy for Surveys

In this paper we propose an instrument for collecting sensitive data that allows for each participant to customize the amount of information that she is comfortable revealing. Current methods adopt a uniform approach where all subjects are afforded the same privacy guarantees; however, privacy is a highly subjective property with intermediate points between total disclosure and non-disclosure: each respondent has a different criterion regarding the sensitivity of a particular topic. The method we propose empowers respondents in this respect while still allowing for the discovery of interesting findings through the application of well-known inferential procedures.

Combining historical and preliminary information to obtain timely time series data

Abstract A method is presented to improve the precision of timely data, which are published when final data are not yet available. Explicit statistical formulae, equivalent to Kalman filtering, are derived to combine historical with preliminary information. The application of these formulae is validated by the data, through a statistical test of compatibility between sources of information. A measure of the share of precision of each source of information is also derived. An empirical example with Mexican economic data serves to illustrate the procedure.

ARIMA forecasts with restrictions derived from a structural change

Abstract Some time series models, which account for a structural change either in the deterministic or in the stochastic part of an arima model are presented. The structural change is assumed to occur during the forecast horizon of the series and the only available information about this change, besides the time point of its occurrence, is provided by only one or two linear restrictions imposed on the forecasts. Formulas for calculating the variance of the restricted forecasts as well as some other statistics are derived. The methods here suggested are illustrated by means of empirical examples.

Data graduation based on statistical time series methods

On the basis of some suitable assumptions, we show that the best linear unbiased estimator of the true mortality rates has the form of Whittakers solution to the graduation problem. Some statistical tools are also proposed to help reducing subjectivity when graduating a dataset.

Rapid Estimates of Mexico’s Quarterly GDP

This work presents ap rocedure for creating at imely estimation of Mexico’s quarterly GDP with the aid of Vector Auto-Regressive models. The estimates consider historical GDP data up to the previous quarter as well as the most recent figures available for two relevant indices of Mexican economic activity and other potential predictors of GDP. We obtain two timely estimates of the Grand Economic Activities and Total GDP. Their corresponding delays are at most 15 days and 30 days respectively from the end of the reference quarter, while the first official GDP figure is delayed 52 days. We follow ab ottom-up approach that imitates the official calculation procedure applied in Mexico. Empirical validation is carried out with both in-sample simulations and in real time. The mean error of the 30-day delayed estimate of total GDP is 0.13% and its root mean square error is 0.67%. These figures compare favorably with those of no-change models.