Page 211 - DMGT404 RESEARCH_METHODOLOGY

Unit 10: Time Series

This form simplifies the calculations substantially compared to the previous formulas. The Notes
code, however, that allows to set x = 0 must incorporate the integrity of a unit distance series.
Thus if the series is odd-numbered, the midpoint is set equal to zero and the code completed by
negative and positive unit distances of x = 1 where each x unit stands for one year or other time
period. If the series is even-numbered, let us say it ran from 1990 to 1999, the two midpoints
(1994/1995) are set equal to -1 and +1, respectively. Since there is now a distance of x = 2 between
+ 1 (-1, 0, +1), the code continues by negative and positive units distance of x = 2 where each x unit
stands for one-half year or other time period.

5.59
Then a = = 6.211
9
S xy
b = = 1.12
S x 2
and Y = 6.211 + 1.12 x
c
origin 1995
x in 1 year units

The regression equation is plotted in Figure 10.2. Note that in the case of time series analysis, the
origin of the code and the x units must be defined as part of the regression equation. In our
problem the investor would like to obtain a dividend forecast for 2001. Since the origin is 1995
(x = 0) and x = 1 year units, the code for 2001 is x = 6. Therefore the forecast is yc = 6.211+1.12 (6)
= 12.9. If the time series had been even numbered, let us say that dividend payments for 1990
had been included in the forecasting study, the definition under the regression equation would
have read
origin 1994/95
x in 6 month units.
Thus, we know that for 1995, x=1; and since we must use x=2 units for each year, the code value
for 2001 would be x=13. Once the yc value has been obtained, b is tested for significance and the
95% confidence interval constructed as previously shown.

Time series analysis is a long-term forecasting tool. Hence, it addresses itself to the trend
component T in our time series equation TS = T + S. In the dividend forecast, b=1.120 was
calculated which means that in the environment that is reflected in the set, smart increased the
dividend payments on a average by 1.12 per year. Let us now turn out attention to the seasonal
variation component that may be present in a time series. A product’s seasonality is shown by
the regularly recurring increases or decreases in sales or production that are caused by seasonal
influences. In the case of some products, their seasonality is quite apparent. As an obvious
example virtually all non-animal agricultural commodities may be cited. Seasonality of other
products may be more difficult to detect. Take hogs in order to stay on the farm. Are they
seasonal? They are lusty breeders and could not care less about seasonal influences. Yet, there is
an induced season by the corn harvest. If corn is plentiful and cheap, farmers raise more hogs.
This is known as the corn-hog cycle. Or take automobiles, Indian manufacturers are used to
introduce major design or technological changes once every generation. This “season” has now
been shortened somewhat. How about computers? There the season even has a special name. It
is called a generation and prior to increased competitive pressures within the industry it used to
be about seven years long. Our stock market investor knows that stock trades on the Stock
Exchanges are seasonal. The daily season is V-shaped starting the trading with a relatively high
volume which tapers off toward the lunch hour to pick up again in the afternoon. And so it goes
with many other products, not ordinarily thought of as being seasonal.

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