R. Deane Terrell

Selecting the Forgetting Factor in Subset Autoregressive Modelling

Conventional methods to determine the forgetting factors in autoregressive (AR) models are mostly based on arbitrary or personal choices. In this paper, we present two procedures which can be used to select the forgetting factor in subset AR modelling. The first procedure uses the bootstrap to determine the value of a fixed forgetting factor. The second procedure starts from this base and applies the time-recursive maximum likelihood estimation to a variable forgetting factor. In one illustration using real exchange rates, we demonstrate the effect of the forgetting factor in subset AR modelling on forecasting of non-stationary time series. In a second illustration, these two procedures are applied to time-update forecasts for a stock market index. Subset AR models not including a forgetting factor act as a set of benchmarks for assessing ex ante forecasting performance, and consistently improved forecasting performance is demonstrated for these proposed procedures. ex ante

A Proposal for: 'Causal Links Between Prices and Exchange Rates'

The primary focus of this study will be an analysis of the causal links, and an assessment of the causal positioning of the significant variables involved in the interactions, between prices and exchange rates. Do exchange rate movements lead to associated price changes or do price changes lead to exchange rate movements? We will further consider whether such responses are short-term or long-term in nature and whether it is possible in a complex sequential process to detect feedback loops. New zero-non-zero patterned vector time series techniques will be used to investigate the emergence of deflation and exchange rate crises.

Multivariate Subset Autoregression - Financial and Economic Forecasting (Chapter 3)

This chapter uses a modified block Choleski decomposition method and tree pruning algorithms to attain the best multivariate subset autoregression for each size (number of non-zero coefficient matrices). Model selection criteria are then employed to select the optimum multivariate subset AR. A Monte Carlo study of these techniques has been investigated to assess their performance, and comparisons of computational efficiency of the proposed procedures are also provided.

A Technical Note on the Fitting of A Multichannel Subset FIR System Within a Potentially Nonstationary Environment, Using the Prewindowed Case - Financial and Economic Forecasting (chapter 9)

The development of a recursive forward and backward time-update algorithm, together with a recursive order-update algorithm, for fitting multichannel subset FIR systems within a potentially nonstationary environment, this method is shown to be efficient and provides linkages between subset AR models and subset FIR systems at consecutive time instants.

Subset Autoregressive Filtering Using the Forgetting Factor for Financial Simulations

Statistical filter researchers for time-series systems are often concerned that the coefficients of their established filters may not be constant over time, but vary when the filters are disturbed by changes arising from outside environmental factors. This concern has motivated researchers to develop sequential estimation algorithms that allow for the coefficients to evolve, such as a recursive estimation of an autoregressive (AR) filter [see Hannan and Deistler (1988)], and a recursive updating procedure for the training process of a multiplayer neural network [see Azimi-Sadjadi et al (1993)]. These studies utilise the fixed forgetting factor (henceforth called the forgetting factor) in the filtering and simulations of nonstationary time series. Conventional methods for determining the forgetting factor for AR filters are mostly based on arbitrary or personal choices. In this paper we use the bootstrap to select the forgetting factor for financial simulations. We also apply the forgetting factor to a time-update recursive algorithm for subset autoregressive filtering. In one illustration using real exchange rates, we demonstrate in Section 4.1 the effect of the forgetting factor in subset AR filtering on ex ante forecasting of nonstationary financial time series. In a second illustration the time-update recursions are applied in Section 4.2 to detect the direct cause-and-effect relationships between the movements of the Euros exchange rate and the money supply.

Testing Purchasing Power Parity in the Framework of Vector Error Correction Modelling - Financial and Economic Forecasting (Chapter 14)

In this chapter, the necessary condition and the necessary and sufficient condition for purchasing power parity (PPP) are sequentially tested for fourteen bilateral exchange rates. This test is undertaken in the framework of subset vector error correction modelling (VECM) with zero coefficients. This approach is different from the unit root based methods and the results are promising. Of the fourteen exchange rates tested, we find support for the necessary condition for PPP in half of them. The necessary and sufficient condition for PPP is then tested using both a bootstrap procedure and an F test. This condition is consistently accepted for three of the seven exchange rates investigated.

Testing for Purchasing Power Parity and Efficiency in the Taiwan Foreign Exchange Market - Financial and Economic Forecasting (chapter 13)

In this chapter, the hypotheses of purchasing power parity (PPP) and market efficiency are tested for the bilateral exchange rate between the New Taiwan (N.T.) and the US dollar. Different test results lead to the conclusion that, a PPP relationship over the long term cannot be rejected confidently. Furthermore, an error correction analysis indicates that this long-term relationship may be helpful in explaining short-term movements in the exchange rate. For testing the efficiency of Taiwans foreign exchange market, the relationship between the spot rate and forward rates is examined for 10-, 30- and 90-day contracts was examined using daily observations. The forward premium is spilt into two components, one due to risk and the other due to a forecasting error. Over the two consecutive sample periods examined (1 May 1992 to 15 February 1993, and 16 February to 31 December 1993) the results are suggestive of a time-varying risk premium in the former period. However, efficiency was found to be acceptable for the 30- and 90-day contracts during the latter sample period.

A Note on the Sequential Fitting of Multichannel Subset Autoregressions Using the Prewindowed Case - Financial and Economic Forecasting (Chapter 7)

In this chapter, an efficient adaptive algorithm for multichannel subset autoregression identification using the prewindowed case is developed. After the initialization is carried out by the direct method, the optimum multichannel subset autoregression at each time instant is selected by employing the proposed recursions in conjunction with a model selection criterion.

A Re-examination of Causality Relationships in Australian Wage Inflation and Minimum Award Rates - Using Multivariate Subset Autoregressive Modelling with Constraints - Financial and Economic Forecasting (chapter 11)

In this chapter, a vector subset autoregressive process is fitted using a block modified Choleski decomposition method and a leaps-and-bounds algorithm to attain the best subset autoregression for each size (number of non-zero coefficient matrices). Model selection criteria are then employed to select the optimum subset AR. (See Penm and Terrell, 1982.) In this chapter the above approach is extended to select the optimum multivariate subset autoregression with constraints, putting the final optimal model in ideal form for detecting Granger causality patterns. The vector system comprising the variables included in the 1981 analysis by Fels and Tran Van Hoa (i.e. Average Weekly Earnings, Consumer Price Index. Index of Minimum Wage Rates, demand for labor, and a strikes variable) is re-examined for the period 1953-76 by using the proposed algorithm, and direct and indirect causal relationships are established.

Using the Bootstrap as an Aid in Choosing the Approximate Representation for Vector Time Series - Financial and Economic Forecasting (Chapter 6)

In this chapter, a procedure is presented to use the bootstrap in choosing the best approximation in terms of forecasting performance for the equivalent state-space representation of a vector autoregressive model. It is found that the proposed procedure, which uses each approximants forecasting performance, can enhance considerably an approach based simply on the estimated Hankel singular values.