Short Time Series Data Research Articles

Factors Affecting the Time Series Bias in Stock–Recruitment Relationships and the Interaction Between Time Series and Measurement Error Bias

The stock–recruitment relationship (SRR) and the recruitment to spawning stock relationship (RSR) of the tiger prawn (Penaeus esculentus) in Exmouth Gulf, Western Australia, were used to examine the time series bias and measurement error bias by Monte Carlo simulations. The bias of the SRR parameters was decreased by adding environmental variables which reduced the variation about the SRR. However, because of the many variables which may be tested and the short time series of data usually available, one needs to be careful about possible spurious correlations. The variation about the RSR also needs to be taken into account, since it has an inverse relationship with the bias in the SRR. Simulating the effect of measurement error as well as the random variation about the SRR and RSR helps to determine the possible combinations of measurement error and random variation which may result in the observed variation about the SRR and RSR. These simulations also indicate that there is an interaction between measurement error and random variation about the SRR/RSR on the bias of the parameters of the SRR. This suggests that the time series bias and measurement error should be investigated simultaneously.

Interpretation of coherence estimates determined for time series of limited length

Coherence of multichannel time series data has been calculated by the method of G. C. Carter and J. F. Ferrie [A Coherence and Cross Spectrum Estimation Program, Programs for Digital Signal Processing (IEEE,New York,1979), No. 2.3‐1‐18]. The properties of this statistic has been contrasted through simulation studies at known noise levels for short and long time series through a range of 40 data segments. Results at less than eight data segments are shown to be difficult to interpret; however, modest improvements in the coherence estimate can be made by adjustments indicated by these studies. A method of calculating coherence estimates through a technique referred to as frequency bin averaging is described. The results obtained are contrasted with the conventional method of Carter. Although reliable estimation of coherence for short time series data (transient data) is difficult to obtain in the conventional sense, the comparisons made should provide a basis for interpretation of coherence estimates as well as suggest corrections that may be applied to relatively short time series sequences. [Work supported by NORDA.]

The Estimation of Spectra and Cross-Spectra on Short Time Series Data

IN HIS RECENT BOOK [20, (Chapters 4, 5)] Professor Hannan has mnade an extensive theoretical study on the asymptotic properties of the multivariate-analytic estimators composed of the direct Fourier Transforms of time series data as contrasted to the estimators obtained through the autocovariances.2 The present paper is concerned with these estimators for the case in which short time series covering, say, 30 to 200 time points have to be dealt with. The direct Fourier transforms of data are adopted as the basic material, not because of speedy computations (Fast Fourier transform) to obtain them, which does not matter much in the presenit case, but because of the ease which they introduce in devising and understanding the estimators in the framework of standard multivariate analysis. We exploit, in particular, the closeness to diagonality of the covariance matrix of the transforms over the multi-frequency points.3 Thus a solution is proposed for a well known problem in the field, that is, how to recover the loss of degrees of freedom caused by a simple data window which has to be used to eliminate the leakages from enormous peaks located at frequencies distant from the one of interest. An empirical study demonstrates that the proposed method is extremely effective in estimating spectra and cross-spectra of economic time series data that are frequently used in econometric studies, say, 15 years, quarterly data. It frees us fromn bothering too much with the prewhitening, and, perhaps it does away with the seasonal adjustment. The present author's conclusion as to the required length of data is contrary to the view expressed in Hannan [20], and, in fact, the present study might contribute to enlarging the applicability of econometric, spectral methods to the development of which