Methods for national population forecasts: a review

"Three widely used classes of methods for forecasting national populations are reviewed: demographic accounting/cohort-component methods for long-range projections, statistical time series methods for short-range forecasts, and structural modeling methods for the simulation and forecasting of the effects of policy changes. In each case, the major characteristics, strengths, and weaknesses of the methods are described. Factors that place intrinsic limits on the accuracy of population forecasts are articulated. Promising lines of additional research by statisticians and demographers are identified for each class of methods and for population forecasting generally."     

Forecasting aggregate period-specific birth rates: the time series properties of a microdynamic neoclassical model of fertility

"This article demonstrates the value of microdata for understanding the effect of wages on life cycle fertility dynamics. Conventional estimates of neoclassical economic fertility models obtained from linear aggregate time series regressions are widely criticized for being nonrobust when adjusted for serial correlation. Moreover, the forecasting power of these aggregative neoclassical models has been shown to be inferior when compared with conventional time series models that assign no role to wages. This article demonstrates that, when neoclassical models of fertility are estimated on microdata using methods that incorporate key demographic restrictions and when they are properly aggregated, they have considerable forecasting power." Data are from the 1981 Swedish Fertility Survey.     

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.     

Forecasting interstate migration with limited data: a demographic-economic approach

"The limitations of available migration data preclude a time-series approach of modeling interstate migration [in the United States]. The method presented here combines aspects of the demographic and economic approaches to forecasting migration in a manner compatible with existing data. Migration rates are modeled to change in response to changes in economic conditions. When applied to resently constructed data on migration based on income tax returns and then compared to standard demographic projections, the demographic-economic approach has a 20% lower total error in forecasting net migration by state for cohorts of labor-force age."     

Forecasting functional time series

We propose forecasting functional time series using weighted functional principal component regression and weighted functional partial least squares regression. These approaches allow for smooth functions, assign higher weights to more recent data, and provide a modeling scheme that is easily adapted to allow for constraints and other information. We illustrate our approaches using age-specific French female mortality rates from 1816 to 2006 and age-specific Australian fertility rates from 1921 to 2006, and show that these weighted methods improve forecast accuracy in comparison to their unweighted counterparts. We also propose two new bootstrap methods to construct prediction intervals, and evaluate and compare their empirical coverage probabilities.     

Forecasting functional time series using weighted likelihood methodology

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).     

Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.     

Spatial modelling of the two‐party preferred vote in Australian federal elections: 2001–2016

We examine the relationships between electoral socio‐demographic characteristics and two‐party preferences in the six Australian federal elections held between 2001 and 2016. Socio‐demographic information is derived from the Australian Census which occurs every 5 years. Since a census is not directly available for each election, an imputation method is employed to estimate census data for the electorates at the time of each election. This accounts for both spatial and temporal changes in electoral characteristics between censuses. To capture any spatial heterogeneity, a spatial error model is estimated for each election, which incorporates a spatially structured random effect vector. Over time, the impact of most socio‐demographic characteristics that affect electoral two‐party preference do not vary, with age distribution, industry of work, incomes, household mobility and relationships having strong effects in each of the six elections. Education and unemployment are among those that have varying effects. All data featured in this study have been contributed to the eechidna R package (available on CRAN).     

Modelling and forecasting by wavelets, and the application to exchange rates

This paper investigates the modelling and forecasting method for non-stationary time series. Using wavelets, the authors propose a modelling procedure that decomposes the series as the sum of three separate components, namely trend, harmonic and irregular components. The estimates suggested in this paper are all consistent. This method has been used for the modelling of US dollar against DM exchange rate data, and ten steps ahead (2 weeks) forecasting are compared with several other methods. Under the Average Percentage of forecasting Error (APE) criterion, the wavelet approach is the best one. The results suggest that forecasting based on wavelets is a viable alternative to existing methods.     

Out-of-Sample Forecast Performance as a Test for Nonlinearity in Time Series

This article uses a local-information, near-neighbor forecasting methodology as a prediction test for evidence of a noisy, chaotic data-generating process underlying the Divisia monetary-aggregate series. Using a nonparametric method known to perform well with low-dimensional chaotic processes infected by noise, accompanied by a robust test of forecast performance evaluation, we compare out-of-sample forecasting accuracy from the local-information method to forecasting accuracy from the best fitting global linear model. Our results fail to substantiate previous claims for determinism in the Divisia monetary-aggregate series because the degree of forecast improvement obtained by the local-information method is not consistent with the hypothesis of a low-dimensional attractor underlying the Divisia data.     

Observable trend-projecting state-space models

Much attention has focused in recent years on the use of state-space models for describing and forecasting industrial time series. However, several state-space models that are proposed for such data series are not observable and do not have a unique representation, particularly in situations where the data history suggests marked seasonal trends. This raises major practical difficulties since it becomes necessary to impose one or more constraints and this implies a complicated error structure on the model. The purpose of this paper is to demonstrate that state-space models are useful for describing time series data for forecasting purposes and that there are trend-projecting state-space components that can be combined to provide observable state-space representations for specified data series. This result is particularly useful for seasonal or pseudo-seasonal time series. A well-known data series is examined in some detail and several observable state-space models are suggested and compared favourably with the constrained observable model.     

Nonparametric forecasting: a comparison of three kernel-based methods

In this paper the use of three kernel-based nonparametric forecasting methods - the conditional mean, the conditional median, and the conditional mode -is explored in detail. Several issues related to the estimation of these methods are discussed, including the choice of the bandwidth and the type of kernel function. The out-of-sample forecasting performance of the three nonparametric methods is investigated using 60 real time series. We find that there is no superior forecast method for series having approximately less than 100 observations. However, when a time series is long or when its conditional density is bimodal there is quite a difference between the forecasting performance of the three kernel-based forecasting methods.     

Observable trend-projecting state-space models

Much attention has focused in recent years on the use of state-space models for describing and forecasting industrial time series. However, several state-space models that are proposed for such data series are not observable and do not have a unique representation, particularly in situations where the data history suggests marked seasonal trends. This raises major practical difficulties since it becomes necessary to impose one or more constraints and this implies a complicated error structure on the model. The purpose of this paper is to demonstrate that state-space models are useful for describing time series data for forecasting purposes and that there are trend-projecting state-space components that can be combined to provide observable state-space representations for specified data series. This result is particularly useful for seasonal or pseudo-seasonal time series. A well-known data series is examined in some detail and several observable state-space models are suggested and compared favourably with the constrained observable model.     

Random Level-Shift Time Series Models,ARIMA Approximations,and Level-Shift Detection

The main purpose of this article is to assess the performance of autoregressive integrated moving average (ARIMA) models when occasional level shifts occur in the time series under study. A random level-shift time series model that allows the level of the process to change occasionally is introduced. Between two consecutive changes, the process behaves like the usual autoregressive moving average (ARMA) process. In practice, a series generated from a random level-shift ARMA (RLARMA) model may be misspecified as an ARIMA process. The efficiency of this ARIMA approximation with respect to estimation of current level and forecasting is investigated. The results of examining a special case of an RLARMA model indicate that the ARIMA approximations are inadequate for estimating the current level, but they are robust for forecasting future observations except when there is a very low frequency of level shifts or when the series are highly negatively correlated. A level-shift detection procedure is presented to handle the low-frequency level-shift phenomena, and its usefulness in building models for forecasting is demonstrated.     

Multistep ahead forecasting of vector time series

This article develops the theory of multistep ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past by developing the forecast filters and the forecast error filters explicitly. We also provide formulas for forecasting from a finite data sample. This latter application can be accomplished by using large matrices, which remains practicable when the total sample size is moderate. Expressions for the mean square error of forecasts are also derived and can be implemented readily. The flexibility and generality of these formulas are illustrated by four diverse applications: forecasting euro area macroeconomic aggregates; backcasting fertility rates by racial category; forecasting long memory inflation data; and forecasting regional housing starts using a seasonally co-integrated model.     

Analyzing Permanent and Transient Influences in Multiple Time Series Models

Several multiple time series models are developed and applied to the analysis and forecasting of the M1 and M2 money supply aggregates. These models feature a decomposition of the time series into permanent and transient influences or components. This decomposition appears to enhance forecasting accuracy and is associated with a variance-covariance allocation parameter that is also estimated from the data. Conditional maximum likelihood estimates for model parameters are presented as well as a numerical algorithm that is an adaptation of Marquardt's algorithm.     

Beta seasonal autoregressive moving average models

In this paper, we introduce the class of beta seasonal autoregressive moving average (βSARMA) models for modelling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha AV and Cribari-Neto F. Beta autoregressive moving average models. Test. 2009;18(3):529–545] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix. We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.     

Sampling the Future: A Bayesian Approach to Forecasting From Univariate Time Series Models

The Box–Jenkins methodology for modeling and forecasting from univariate time series models has long been considered a standard to which other forecasting techniques have been compared. To a Bayesian statistician, however, the method lacks an important facet—a provision for modeling uncertainty about parameter estimates. We present a technique called sampling the future for including this feature in both the estimation and forecasting stages. Although it is relatively easy to use Bayesian methods to estimate the parameters in an autoregressive integrated moving average (ARIMA) model, there are severe difficulties in producing forecasts from such a model. The multiperiod predictive density does not have a convenient closed form, so approximations are needed. In this article, exact Bayesian forecasting is approximated by simulating the joint predictive distribution. First, parameter sets are randomly generated from the joint posterior distribution. These are then used to simulate future paths of the time series. This bundle of many possible realizations is used to project the future in several ways. Highest probability forecast regions are formed and portrayed with computer graphics. The predictive density's shape is explored. Finally, we discuss a method that allows the analyst to subjectively modify the posterior distribution on the parameters and produce alternate forecasts.     

Scenarios,uncertainty and conditional forecasts of the world population

This study is concerned with the methods available for the forecasting of future trends in the world's population. Particular attention is given to the problem of the uncertainties that these forecasts include. "The purpose of this paper is to show how subjective and data-based probabilistic assessments of error can be combined, to give a user a realistic assessment of the uncertainty of demographic forecasts, and to apply these concepts to forecasts of the world population. Moreover, we shall show how conditional forecasts can provide a simple conceptual framework in which to view scenarios. They can be particularly useful in the evaluation of proposed policies. Indeed, the so-called environmental impact assessments...that are now mandatory in many countries for major construction projects typically contain elements of conditional forecasting." The concepts discussed are illustrated by comparing a scenario of future global population growth prepared at the Institute of Applied Systems Analysis with a UN population projection.