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A time series analysis of the gilt-edged market
Omega, Vol. 1, No. 5 SAMPLE
SIZE FOR COMPARATIVE EXPERIMENTS
SIMULATION
ELDREDGE DL (1973) A study of sample size for eomputor simulation experiments. 1973 Annual Meeting of Southeastern Chapter of the American Institute of Decision Sciences. Paper available from David L Eidredge, School of Business, University of Evansville, Evansville, Indiana, U.S.A.
M ANY simulation experiments are conducted in order to determine the "best" of a set of possible systems for accomplishing some objective. If these systems can be characterized by a small number of quantitative variables, the determination of the best system might be accomplished through a stochastic search procedure. Such a procedure may not require that simulation experiments be performed with all the alternative systems being considered. Frequently however, the alternative systems can only be classified according to a nominal scale. This requires that some experiments be conducted with each alternative if the best system is to be identified. Faced with this problem many experimenters simply conduct some number of experiments, say n, with each of say m alternative systems. Based on the results of some outcome measure for each of these m times n experiments, they then identify the best system. However, if the experimenter's objective is only to pick the best system and he is not concerned with (1) Estimating the expected outcome for each system, or (2) Ranking the alternative systems according to their relative expected outcomes, the total number of simulation experiments required to maintain a specified significance level may be considerably less than m times n. The purpose of this paper is to describe a sequential procedure for conducting simulation experiments which does reduce the number of required experiments. In addition, we investigate the size of this reduction for various possible situations. Abstracted by David L Eldredge, University of Evansville, Indiana, U.S.A.
TIME
SERIES
ANALYSIS OF THE MARKET
GILT-EDGED
HARRIS RG (1972) A time series analysis of the gUt-edged market. MSc. Thesis, Lyon Playfair Library, Imperial College of Science and Technology, London SW7 2AZ, England.
TH:s report describes an attempt to use the statistical methods of time series analysis, and in particular the more recent advances, in the analysis of the movement of gross redemption yields of gilt-edged stocks. The emphasis is on 633
Abstracts
the use and discussion on the statistical methods employed rather than the background of the gilt-edged market or the practical interpretation of the results. Two major methods are discussed: correlation in the time domain developed by Box and Jenkins [1] and spectral analysis in the frequency domain developed by Jenkins and Watts [2]. It was found that these two approaches complemented each other, investigating different aspects of the data. The first method indicated that the time series of daily gilt-edged gross redemption yields should exhibit short-term random length cycles, i.e. the random walk hypothesis is substantiated. However the second method did indicate the existence of significant cycles in the series at 7 and 10-12 days past, and that inclusion of these yields might improve prediction. Analysis of runs also indicated the existence of a cycle of 10-12 days length. The identification of significant longer-term cycles would however have been improved if more data had been available. Work is also described on the transfer function, that is, the prediction of the movement of one stock through an examination of the movement of another stock, but the results are not conclusive. Weekly observed yields were also examined and here the method of spectral analysis was found to be of much more use. An autoregressive model was constructed which included five different lagged terms. Finally the implications of the daily model with reference to jobbing switches are discussed. It was found that if the Box and Jenkins' model were to be used, switching would be carried out far more frequently than it is at the present time. This substantiates the existence of short-term random cycles in the data. REFERENCES 1. Box GEP and JENKINS GM (1970) Time Series Analysis, Forecasting and Control. Holden Day, San Francisco. 2. JENKINS GM and WATTS DG (1968) Spectral Analysis and its Applications. Holden Day, San Francisco. Abstracted by RB Flavell, Imperial College, London.
AN
ANALYSIS
OF THE CHARACTERISTICS LABEL ACTIVITY
OF OWN
JENKINS JH (1971) An analysis of the characteristics of own label activity, with particular reference to the United Kingdom Economy. MSe. Dissertation, Department of Management Sciences, U.M.I.S.T., Manchester, England.
MOST own label products in the grocery trade were found to be standard products bought frequently by the consumer, products which had been on the market for some time, and products for which there was little real product differentiation vis-a-vis the corresponding manufacturer brands. These characteristics result mainly from the fact that retailers usually wait until turnover in the product has reached a substantial level before introducing an own label. 634
SIZE FOR COMPARATIVE EXPERIMENTS
SIMULATION
ELDREDGE DL (1973) A study of sample size for eomputor simulation experiments. 1973 Annual Meeting of Southeastern Chapter of the American Institute of Decision Sciences. Paper available from David L Eidredge, School of Business, University of Evansville, Evansville, Indiana, U.S.A.
M ANY simulation experiments are conducted in order to determine the "best" of a set of possible systems for accomplishing some objective. If these systems can be characterized by a small number of quantitative variables, the determination of the best system might be accomplished through a stochastic search procedure. Such a procedure may not require that simulation experiments be performed with all the alternative systems being considered. Frequently however, the alternative systems can only be classified according to a nominal scale. This requires that some experiments be conducted with each alternative if the best system is to be identified. Faced with this problem many experimenters simply conduct some number of experiments, say n, with each of say m alternative systems. Based on the results of some outcome measure for each of these m times n experiments, they then identify the best system. However, if the experimenter's objective is only to pick the best system and he is not concerned with (1) Estimating the expected outcome for each system, or (2) Ranking the alternative systems according to their relative expected outcomes, the total number of simulation experiments required to maintain a specified significance level may be considerably less than m times n. The purpose of this paper is to describe a sequential procedure for conducting simulation experiments which does reduce the number of required experiments. In addition, we investigate the size of this reduction for various possible situations. Abstracted by David L Eldredge, University of Evansville, Indiana, U.S.A.
TIME
SERIES
ANALYSIS OF THE MARKET
GILT-EDGED
HARRIS RG (1972) A time series analysis of the gUt-edged market. MSc. Thesis, Lyon Playfair Library, Imperial College of Science and Technology, London SW7 2AZ, England.
TH:s report describes an attempt to use the statistical methods of time series analysis, and in particular the more recent advances, in the analysis of the movement of gross redemption yields of gilt-edged stocks. The emphasis is on 633
Abstracts
the use and discussion on the statistical methods employed rather than the background of the gilt-edged market or the practical interpretation of the results. Two major methods are discussed: correlation in the time domain developed by Box and Jenkins [1] and spectral analysis in the frequency domain developed by Jenkins and Watts [2]. It was found that these two approaches complemented each other, investigating different aspects of the data. The first method indicated that the time series of daily gilt-edged gross redemption yields should exhibit short-term random length cycles, i.e. the random walk hypothesis is substantiated. However the second method did indicate the existence of significant cycles in the series at 7 and 10-12 days past, and that inclusion of these yields might improve prediction. Analysis of runs also indicated the existence of a cycle of 10-12 days length. The identification of significant longer-term cycles would however have been improved if more data had been available. Work is also described on the transfer function, that is, the prediction of the movement of one stock through an examination of the movement of another stock, but the results are not conclusive. Weekly observed yields were also examined and here the method of spectral analysis was found to be of much more use. An autoregressive model was constructed which included five different lagged terms. Finally the implications of the daily model with reference to jobbing switches are discussed. It was found that if the Box and Jenkins' model were to be used, switching would be carried out far more frequently than it is at the present time. This substantiates the existence of short-term random cycles in the data. REFERENCES 1. Box GEP and JENKINS GM (1970) Time Series Analysis, Forecasting and Control. Holden Day, San Francisco. 2. JENKINS GM and WATTS DG (1968) Spectral Analysis and its Applications. Holden Day, San Francisco. Abstracted by RB Flavell, Imperial College, London.
AN
ANALYSIS
OF THE CHARACTERISTICS LABEL ACTIVITY
OF OWN
JENKINS JH (1971) An analysis of the characteristics of own label activity, with particular reference to the United Kingdom Economy. MSe. Dissertation, Department of Management Sciences, U.M.I.S.T., Manchester, England.
MOST own label products in the grocery trade were found to be standard products bought frequently by the consumer, products which had been on the market for some time, and products for which there was little real product differentiation vis-a-vis the corresponding manufacturer brands. These characteristics result mainly from the fact that retailers usually wait until turnover in the product has reached a substantial level before introducing an own label. 634