Temporal disaggregation and restricted forecasting of multiple population time series

This article presents some applications of time-series procedures to solve two typical problems that arise when analyzing demographic information in developing countries: (1) unavailability of annual time series of population growth rates (PGRs) and their corresponding population time series and (2) inappropriately defined population growth goals in official population programs. These problems are considered as situations that require combining information of population time series. Firstly, we suggest the use of temporal disaggregation techniques to combine census data with vital statistics information in order to estimate annual PGRs. Secondly, we apply multiple restricted forecasting to combine the official targets on future PGRs with the disaggregated series. Then, we propose a mechanism to evaluate the compatibility of the demographic goals with the annual data. We apply the aforementioned procedures to data of the Mexico City Metropolitan Zone divided by concentric rings and conclude that the targets established in the official program are not feasible. Hence, we derive future PGRs that are both in line with the official targets and with the historical demographic behavior. We conclude that growth population programs should be based on this kind of analysis to be supported empirically. So, through specialized multivariate time-series techniques, we propose to obtain first an optimal estimate of a disaggregate vector of population time series and then, produce restricted forecasts in agreement with some data-based population policies here derived.     

Determining the Number of Primitive Shocks in Factor Models

Personal consumption expenditures (PCE) in the National Income and Product Accounts are often used to investigate whether the time series properties of consumption are consistent with the permanent-income/life-cycle hypotheses. In this article, I address the issue of the general quality of the PCE data and its definitional consistency with the typical model of the intertemporal allocation of consumption. I find that, in terms of the population coverage and the consumption concept, the raw PCE data are unsuitable for the analysis of the permanent-income/life-cycle hypotheses. More fundamentally, adjustments to the data to provide greater consistency with the theory alter critical conclusions concerning the time series properties of consumption.     

On the asymptotic distribution of a simple unit root test for trending and breaking series

In this paper, we derive the asymptotic distribution of Popp's (2008) innovational outlier unit root test for trending series with a break. The results of Zivot and Andrews (1992) are applied to provide the limiting results of these new test statistics. We tabulate their asymptotic and finite sample critical values, and illustrate the use of the new statistics with an application to the unemployment rate series for 23 OECD countries.     

Logarithmic and power transformations in the context of fractionally integrated processes

In this article we examine the effect that logarithmic and power transformations have on the order of integration in raw time series. For this purpose, we use a version of the tests of Robinson (1994) that permits us to test I ( d ) statistical models. The results, obtained via Monte Carlo, show that there is no effect in the degree of dependence of the series when this type of transformations are employed, resulting thus in useful mechanisms to be applied when a more plausible economic interpretation of the data is required.     

Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence

This article investigates the possibility, raised by Perron and by Rappoport and Reichlin, that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike those authors, we treat the break date as unknown a priori. Asymptotic distributions are developed for recursive, rolling, and sequential tests for unit roots and/or changing coefficients in time series regressions. The recursive and rolling tests are based on changing subsamples of the data. The sequential statistics are computed using the full data set and a sequence of regressors indexed by a “break” date. When applied to data on real postwar output from seven Organization for Economic Cooperation and Development countries, these techniques fail to reject the unit-root hypothesis for five countries (including the United States) but suggest stationarity around a shifted trend for Japan.     

Hierarchical clustering and matrix completion for the reconstruction of world input–output tables

Multi-regional input–output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (parts of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and matrix completion with a LASSO-like nuclear norm penalty, to predict missing entries of a partially unknown I/O matrix. Through analyses based on both real-world and synthetic I/O matrices, we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input–Output Database (WIOD) tables—which are an example of industry-by-industry I/O tables—is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.

     

Maximum entropy extreme‐value seasonal adjustment

Some economic series in small economies exhibit meagre (i.e. non‐positive) values, as well as seasonal extremes. For example, agricultural variables in countries with a distinct growing season may exhibit both of these features. Multiplicative seasonal adjustment typically utilises a logarithmic transformation, but the meagre values make this impossible, while the extremes engender huge distortions that render seasonal adjustments unacceptable. To account for these features, we propose a new method of extreme‐value adjustment based on the maximum entropy principle, which results in replacement of the meagre values and extremes by optimal projections that utilise information from the available time series dynamics. This facilitates multiplicative seasonal adjustment. The method is illustrated in the New Zealand agricultural series.     

The change in real interest rate persistence in OECD countries: evidence from modified panel ratio tests

This study examines whether real interest rates exhibit changes in persistence for a panel of Organization of Economic Cooperation and Development countries. The findings show that for long-term real interest rates there are changes in persistence from I(0) to I(1). For short-term real interest rates, the results display the absence of changes in persistence, while under cross-sectional dependence there is only weak evidence of changes in persistence from I(1) to I(0). The evidence of changes in persistence when the direction is considered unknown is even weaker.     

Custom Epoch Estimation for Surveys

The paper provides a method for generating epoch estimates for time series survey data, allowing for different periods of time (or even point estimates) according to user demand. The method uses a modified kriging estimator, which suppresses the contribution of sampling error variability in order to guarantee that custom epoch estimates have an interpolation property. For the veteran population variable of the American Community Survey, we utilize a simple Brownian Motion model of the population process and derive the modified kriging estimator for this case. The tuning parameters of this population model can be calibrated to the data via simple formulas. We illustrate the application of this method to the generation of point estimates of veteran population, an important objective for Veterans Affairs.     

Simulation and quality of a synthetic close-to-reality employer–employee population

It is of essential importance that researchers have access to linked employer–employee data, but such data sets are rarely available for researchers or the public. Even in case that survey data have been made available, the evaluation of estimation methods is usually done by complex design-based simulation studies. For this aim, data on population level are needed to know the true parameters that are compared with the estimations derived from complex samples. These samples are usually drawn from the population under various sampling designs, missing values and outlier scenarios. The structural earnings statistics sample survey proposes accurate and harmonized data on the level and structure of remuneration of employees, their individual characteristics and the enterprise or place of employment to which they belong in EU member states and candidate countries. At the basis of this data set, we show how to simulate a synthetic close-to-reality population representing the employer and employee structure of Austria. The proposed simulation is based on work of A. Alfons, S. Kraft, M. Templ, and P. Filzmoser [{\em On the simulation of complex universes in the case of applying the German microcensus}, DACSEIS research paper series No. 4, University of Tübingen, 2003] and R. Münnich and J. Schürle [{\em Simulation of close-to-reality population data for household surveys with application to EU-SILC}, Statistical Methods & Applications 20(3) (2011c), pp. 383–407]. However, new challenges are related to consider the special structure of employer–employee data and the complexity induced with the underlying two-stage design of the survey. By using quality measures in form of simple summary statistics, benchmarking indicators and visualizations, the simulated population is analysed and evaluated. An accompanying study on literature has been made to select the most important benchmarking indicators.     

Comment

Using postwar annual data through 1987 from 46 countries, we confirm our earlier finding that the maximum impact (χ) of monetary shocks on real output is negatively correlated across countries with the variance of such shocks (σ ) [the Lucas proposition (LP)]. This holds whether the time series specification for each country is the one we reported in Kormendi and Meguire (1984) (KM), one selected by a Bayesian pretest (BPT) suggested by Poirier's results, or a uniform specification that nests both. Using the LP to restrict the coefficients of monetary shocks in the real output equation significantly improves forecasts of real output growth over the period 1978–1987. Over the same period, predictions of money and real output growth made from the BPT specifications often do not outperform comparable predictions made from the KM specifications.     

SAMPLE SURVEYS VERSUS EXPERIMENTS,CONTROLLED OBSERVATIONS,CENSUSES, REGISTERS,AND LOCAL STUDIES1 2

Can we find some common principle in the three comparisons? Lacking adequate time for a thorough exploration, let me suggest that representation is that common principle. I suggested (section 4) that judgment selection of spatial versus temporal extensions distinguish “longitudinal” local studies from “cross-section” population sampling. We had noted (section 3) that censuses are taken for detailed representation of the spatial dimension but they depend on judgmental selection of the temporal. Survey sampling lacks spatial detail but is spatially representative with randomization, and it can be made timely. Periodic samples can be designed that are representative of temporal extension. Furthermore, spatial and temporal detail can be obtained either through estimation or through cumulated samples [Purcell and Kish 1979, 1980; Kish 1979b, 1981, 1986 6.6]. Registers and administrative records can have good spatial and temporal representation, but representation may be lacking in population content, and surely in representation of variables. Representation of variables and of the relations between variables and over the population are the issues in conflict between surveys, experiments, and observations. This is a deep subject, and too deep to be explored again, as it was in section 2. A final point about limits for randomization to achieve representation through sampling: randomization for selecting samples of variables is beyond me generally, because I cannot conceive of frames for defined populations of variables. Yet we can find attempts at randomized selection of variables: in the selection of items for the consumer price index, also of items for tests of IQ or of achievements. Generally I believe that randomization is the way to achieve representation without complete coverage, and that it can be applied and practised in many dimensions.     

A Method for Seasonally Adjusting Time Series With Variation in the Seasonal Amplitude

The official seasonally adjusted figures of the unemployment series in the Netherlands proved to be unsatisfactory in the years 1976 until 1980 because of the occurrence of a residual seasonal pattern in the adjusted series. There is indication that this failure is due to the presence of variations in the seasonal amplitude of the unemployment series. To improve this unsatisfactory state of affairs further research on methods of seasonal adjustment was undertaken at the Netherlands Central Bureau of Statistics. The outcome, method CPBX11, combines features of two methods that have been used officially, CENSUS X-11 and CPB-1. Since December 1980 the Netherlands Central Bureau of Statistics has used CPBX11 to compute seasonally adjusted labor market series. In this article we review in short the literature on seasonal adjustment and compare the performance of the three procedures referred to above in adjusting the series Unemployment in Construction and Live Births (per 1,000 of the mean population) for the Netherlands. The CPBX11 method yields more satisfactory results, especially for the first series.     

Bias correction for time series factor models

In this paper we work with multivariate time series that follow a Factor Model. In particular, we consider the setting where factors are dominated by highly persistent AutoRegressive (AR) processes and samples that are rather small. Therefore, the factors' AR models are estimated using small sample bias correction techniques. A Monte Carlo study reveals that bias-correcting the AR coefficients of the factors allows to obtain better results in terms of prediction interval coverage. As expected, the simulation shows that bias-correction is more successful for smaller samples. We present the results assuming the AR order and number of factors are known as well as unknown. We also study the advantages of this technique for a set of Industrial Production Indexes of several European countries.     

The sample autocorrelation function of I(1) processes

In case of a random walk the theoretical autocorrelations tend to one asymptotically. The sample autocorrelations, however, may decline rather fast even with large samples. We will explain this observation by deriving the asymptotic distribution that turns out to be closely related to the Dickey-Fuller (1979) distribution. Moreover we discuss the behaviour of the sample autocorrelations of integrated MA(1) and AR(1) processes. In order to prove our results we consider more general I(1) processes and apply the functional central limit theorem injected to time series analysis by Phillips (1987). We obtain unit root tests that are based on autocorrelation estimators of higher lags. We discuss their finite sample behaviour experimentally.     

The Sensitivity of Detrended Long-Memory Processes

Long-memory tests are often complicated by the presence of deterministic trends. Hence, an additional step of detrending the data is necessary. The typical way to detrend a suspected long-memory series is to use OLS or BSP residuals. Applying the method of sensitivity analysis we address the of question of how robust these residuals are in presence of potential long memory components. Unlike short-memory ARMA process long-memory I(d) processes causes sensitivity to OLS/BSP residuals. Therefore, we develop a finite sample measure of the sensitivity of a detrended series based on the residuals. Based on our sensitivity measure we propose a “rule of thumb” for practitioners to choose between the two methods of detrending, has been provided in this article.     

On the exact distribution of the likelihood ratio criterion for testing

The exact null distribution of the likelihood ratio criter- 2 ion for testing the hypothesis H: y = y~; z = a I, a unknown and UQ a given known vector against the alternative A =f H in a p-vari- ate normal population N (y,z) has been derived in the form of Meijer's G-function using mellin integral transform and also in a chisquare series form. Asymptotic behavior of the distribution of -2 log L has also been discussed. Percentage points for p=2(l)10for various level of significance and various degrees of freedom have been computed, but only selected tables have been presented in this paper.     

Comparison of Times Series with Unequal Length in the Frequency Domain

In statistical data analysis it is often important to compare, classify, and cluster different time series. For these purposes various methods have been proposed in the literature, but they usually assume time series with the same sample size. In this article, we propose a spectral domain method for handling time series of unequal length. The method make the spectral estimates comparable by producing statistics at the same frequency. The procedure is compared with other methods proposed in the literature by a Monte Carlo simulation study. As an illustrative example, the proposed spectral method is applied to cluster industrial production series of some developed countries.     

Fractional integration and impulse responses: a bivariate application to real output in the USA and four Scandinavian countries

This article analyzes impulse response functions in the context of vector fractionally integrated time series. We derive analytically the restrictions required to identify the structural-form system. As an illustration of the recommended procedure, we carry out an empirical application based on a bivariate system including real output in the USA and, in turn, in one of the four Scandinavian countries (Denmark, Finland, Norway, and Sweden). The empirical results appear to be sensitive, to some extent, to the specification of the stochastic process driving the disturbances, but generally a positive shock to US output has a positive effect on the Scandinavian countries, which tend to disappear in the long run.