What is trend projection What does a linear trend measure Wh

What is trend projection What does a linear trend measure What is the other most common trend form used in time - series analysis What does this show Which is better Why might a forecast obtained by projecting a past trend into the future give poor results even if past patterns remain unchanged

Solution

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(a) What is trend projection?

Answer : A trend is the behaviour of a certain variable with respect to something , in this case with time. Suppose you want to buy a book on any online website. But its price is changing everyday. So you observe the behaviour of change in the past couple days. And based in this you project that at certain day from now, the price will be minimum. Now this projection of price based on past trends will be called trend projection here.

(b) What does a linear trend measure?

Answer : A linear trend measures the implication if the variable that is the cause is increasing/decreasing linearly with the effect. Consider a hypothetical case where the price of an XYZ book is $2 on Monday. On tuesday its price is increased to $2.2 . On Wednesday its price increases to $2.4 On thursday its price increases to $2.6. Now you can clearly see here that the price of the book is increasing linearly with respect to day. Thus this situation is a good example of linear trend.

In real life situations there are hardly any instances when we observe a linear trend.

What is the other most common trend form used in time-series analysis? What does this show?

Answer : Exponential trend is also a common trend in time series analysis. We generally use this when the rate of increase also increases with the increase in the variable.

Which is better?

Answer : This is totally based on the time span for which we are recording the data and the time when we want the projection of. If we record data regularly and we want the projection of immediately next few days then linear trend should serve better.

(c) Why might a forecast obtained into the future give poor results even if the past patterns remains unchanged?

Answer : If there is a change in any other variable which we have not accounted in forecasting, then the forecast will give poor results even though the past patterns remains unchanged.