Covariance and Correlation
The business section of newspapers give regular reports on movements in interest rates and foreign exchange rates. For example, the following is from the Vancouver Sun (byline: Norma Greenaway, November 26, 1997).
The Bank of Canada nudged its benchmark rate a quarter point to four per cent on Monday. ... The central bank's modest hike ... set off a round of rate increases by the major commercial banks. Beginning today, the prime lending rate -- available only to their most credit-worthy customers -- will climb to 5.5 per cent from 5.25 per cent. Mortgage rates were not immediately affected. ... The dollar strengthened slightly against its U.S. counterpart in the wake of the announcement, closing at 70.57 cents -- up about one-fifth of a cent from its opening.
The above recognizes the important associations between various economic variables. The strength of these associations can be considered by analyzing a data set. A monthly data set with the Canadian chartered bank prime business loan rate, the 5 year mortgage rate and the Canadian/U.S. $ exchange rate was collected from the Statistics Canada CANSIM data base.
The SHAZAM commands that follow first read the data and
assign variable names.
The SHAZAM output can be viewed.
The results show that the estimated correlation between
the prime lending rate and the 5-year mortgage rate is 0.93
(for presentation purposes, the
numerical results have been rounded to 2 decimal places).
The estimated correlation between the prime lending rate and the
Canadian/U.S. $ exchange rate is
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|_SAMPLE 1 204 |_READ (MOBS.txt) DATE PRIME MRATE5 USCAN UNIT 88 IS NOW ASSIGNED TO: MOBS.txt 4 VARIABLES AND 204 OBSERVATIONS STARTING AT OBS 1 |_STAT PRIME MRATE5 USCAN / PCOV PCOR NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM PRIME 204 10.963 3.6408 13.255 4.7500 22.750 MRATE5 204 12.034 2.9599 8.7610 6.9400 21.460 USCAN 204 1.2669 0.83719E-01 0.70089E-02 1.1279 1.4129 CORRELATION MATRIX OF VARIABLES - 204 OBSERVATIONS PRIME 1.0000 MRATE5 0.92975 1.0000 USCAN -0.49047 -0.42991 1.0000 PRIME MRATE5 USCAN COVARIANCE MATRIX OF VARIABLES - 204 OBSERVATIONS PRIME 13.255 MRATE5 10.019 8.7610 USCAN -0.14950 -0.10653 0.70089E-02 PRIME MRATE5 USCAN |_STOP
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