3. The trend equation for newsprint production of WANG Company is T-641.04+0.74x

Question

3. The trend equation for newsprint production of WANG Company is T-641.04+0.74x , where T-monthly production in millions of tons, x-1 in March 1986 and one unit of x- one month. Actual production figures for selected months in 1993 are given below: Month Actual Production March,1993 April,1993 May, 1993 June, 1993 690 708 804 1176 86 101 110 165 a) In which of these months is newsprint production the highest (i) if seasonal variation is incorporated, and (ii)seasonal variation is excluded from consideration. (deseasonalized) b) Which month is the production most typical of the monthly average? c) For May 1993, isolate the effect of each component of a time series: trend, seasonal and cyclical irregular. (Hint: What are the "S", the "T" and "CxI" of May 1993?) Hint: Mar 1986 Mar 1987 May 1993 13

Explanation / Answer

(a) (i) If seasonal variation is incorpated, then the highest newsprint production is in month June.

(ii) If seasonal variation is excluded then the deseasonalized production for

March 1993 = 690 * 100/86 = 802.33

April 1993 = 708 * 100/101 = 701.00

MAy 1993 = 804 * 100/110 = 730.91

June 1993 = 1176 * 100/165 = 712.73

so March month has highest deasonalized sale

(b) Here month of April has the most typical of monthly average.

(c) Here value of x for May 1993 is 12 * (1993 - 1986) + 3 = 12 * 7 + 3 = 87

so Trend component = 641.04 + 0.74 *x = 641.04 + 0.74 * 87 = 705.42

Cyclical irregular = 730.91 - 705.42 = 25.49

Seasonal Component = 804 - 730.91 = 73.09

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