A Multivariate Time Series Approach to Modelling Macroeconomic Sequences

In this paper we discuss a multivariate generalization of autoregressive integrated moving average models. A methodology for constructing multivariate time series models is developed and the derivation of forecasts from such models is considered. A bivariate model for Austrian macroeconomic sequences is constructed. Furthermore it is discussed whether multivariate time series methods can be expected to lead to a significant increase in prediction accuracy for macroeconomic series

The Analysis of Multivariate Time Series with a View to Applications in Hydrology

In this paper we discuss stochastic models for vector processes, in particular the class of multivariate autoregressive moving average models. Special cases of this class have been discussed in the literature on multisite streamflow generation and it is shown how these can be brought into a general framework. An iterative model building procedure, consisting of model specification -- estimation -- diagnostic checking is stressed. Results on model specification are given and it is shown how partial autocovariance matrices can be used to check whether multivariate autoregressive models provide adequate representation for (standardized) streamflow sequences. Furthermore, estimation of parameters in multivariate autoregressive moving average models is discussed and it is pointed out that moment estimators can be inefficient when moving average parameters are present. An approximate maximum likelihood estimation procedure is suggested. In the concluding section, we summarize important practical implications for hydrologists

Adaptivity and Stability of Time Series Models

The effect of interventions on economic variables in the presence of a time dependent noise structure is modelled in this paper. Forecasts from such models are derived and it is discussed whether forecasts from ARIMA time series models are adaptive with respect to interventions such as changes in the level of outliers. An overall criterion to test the stability of the parameters in ARIMA models is derived and applied to three Austrian macroeconomic sequences

Use of Kalman Filtering Techniques when the Parameters of a Regression Relationship are Changing over Time According to a Multivariate ARIMA Process

It is shown how Kalman filtering methodology can be applied to the estimation of the parameters in a regression model, when the parameters are subject to change over time. A multivariate ARIMA model for the parameters of the regression relationship is entertained and it is shown how this model can be brought into the state variable form. Furthermore it is shown how this procedure specializes to various cases already discussed in the literature

Conditions for the Optimality of Exponential Smoothing Forecast Procedures

Exponential smoothing procedures, in particular those recommended by Brown are used extensively in many areas of economics, business and engineering. It is shown in this paper that: (i) Brown's forecasting procedures are optimal in terms of achieving minimum mean square error forecasts only if the underlying stochastic process is included in a limited subclass of ARIMA (p,d,q) processes. Hence, it is shown what assumptions are made when using these procedures. (ii) The implication of point (i) is that the users of Brown's procedures tacitly assume that the stochastic processes which occur in the real world are from the particular restricted subclass of ARIMA (p,d,q) processes. No reason can be found why these particular models should occur more frequently than others. (iii) It is further shown that even if a stochastic process which would lead to Brown's model occurred, the actual methods used for making the forecasts are clumsy and much simpler procedures can be employed

The Multiple Indicator - Multiple Cause Model with Several Latent Variables

A model in which one observes multiple indicators and multiple causes of several latent variables is considered. The parameters of this model are estimated by maximum likelihood and restricted rank regression approaches. Also a likelihood ratio test statistic for testing the validity of the restrictions in the above model is derived

Inference Robustness of ARIMA Models under Non-normality - Special Application to Stock Price Data

Wold's decomposition theorem states that every weakly stationary stochastic process can be decomposed into orthogonal shocks. For practical reasons, however, it is desirable to employ models which use parameters parsimoniously. Box and Jenkins show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terns (ARIMA-models). The Gaussian hypothesis assumes that the shocks follow a normal distribution with fixed mean and variance. In this case the process is characterized by first and second order moments. The normality assumption seems to be reasonable for many kinds of series. However, it was pointed out by Kendall, Mandelbrot, and Fama that particularly for stock price data the distribution of the shocks appears leptokurtic. In this paper we investigate the sensitivity of ARIMA models to non-normality of the distribution of the shocks. We suppose that the distribution function of the shocks is a member of the symmetric exponential power family, which includes the normal as well as leptokurtic and platikurtic distributions. A Bayesian approach is adopted and the inference robustness of ARIMA models with respect to (i) the estimation of parameters, and (ii) the forecasts of future observations is discussed

ARIMA Models and their Use in Modelling Hydrologic Sequences

In recent years there has been considerable interest in building models which preserve the autocorrelation structure of hydrologic sequences. In particular, Markov models, are frequently entertained to describe the time dependence of run-off sequences. In this paper we follow a more general approach. Instead of restricting ourselves to Markov models, we consider the class of autoregressive integrated moving average (ARIMA) models. This broad class of models is capable of representing many time series observed in practice. Since the distribution of the run-off sequences is frequently skewed, one has to transform the data. In this paper we give some thought to the questions of which transformation one should choose. The class of power transformations is discussed in detail

A Note on the Estimation of Polynomial Distributed Lags

Methods of estimation of polynomial distributed lags in econometrics and procedures relating tree ring growth data to climatic and hydrologic data are shown to be equivalent to a method first described by R.A. Fisher in 1924

A New Approach in Energy Demand. Part I: Methodology and Illustrative Examples

A great deal of work has been carried out on the relation between per capita GNP and per capita energy consumption. In this short paper we substitute the structure of GNP to its absolute level. Three sectors were only retained: namely, agriculture, industry, and services (including transportation). The relation between per capita energy consumption and GNP structure explicitly constructed and adjusted on data is a potential in the space of GNP structures