# Trend

Trend is the steady increase or decrease in the value of variable over a long period of time. For example, the steady increase in the price level over the decades is an example of secular trend. Trend represents the long-term direction of the variable in the time series.
Trend is the most important component of time series. It is studied for the following reasons:

1. To describe a historical pattern
2. To project future trends
3. To study other components of time series by identify and eliminate trend from time series.

# Growth rate

Growth rate is the measure of average changes in the value of a variable within a period. It is highly used in business to make future projection of the behavior of the variable in a future time period.

Both growth rate and trend are used for future projections. Therefore, they must have some similarity. But they also have some dissimilarity too.
The similarities and dissimilarities between growth rate and trend are shortly described below-

## Similarities between growth rate and trend:

1. Both trend and growth rate shows the increase or decrease of the variable over the time.
2. They are used to provide a single rate of increase or decrease over the period.
3. They are used to forecast the future level of variable.
4. Usually both trend and growth rate are in the same direction.

## Dissimilarities between trend and growth rate:

1. Trend can be linear or nonlinear, but growth rate is always non-linear.
2. Trend is the steady movement of the variable in the long run, while growth rate is the average rate of change in variable over a definite period
3. Growth rate can be determined in short time periods too but it is difficult to determine trend in short run.
4. Trend is a component of time series, while growth rate is the average change in the time series.

## The similarities and dissimilarities are illustrated with an example below:

The annual sales revenue for XYZ Company for past 7 years are as follows:

 Year 1999 2000 2001 2002 2003 2004 2005 Sales (in lac Tk.) 5 11 17 21 29 34 39

Here the trend equation:
where   y = sales
a = estimated sales in year 0
b = the rate of change in sales every year
t  = time
The following table is prepared for calculation:

From the table:

So required trend equation: y = -0.55 + 5.71t

here, both trend and growth rate shows the increase or decrease of the variable over the time, provide a single rate of increase or decrease over the period. both trend and growth rate are in the same direction. And They can be used to forecast the future level of variable (sales).
Now the difference between growth rate and trend can be easily understood from the following graphs:

Here-
*The trend is linear, but line based on growth rate is non-linear.
*From the calculation below, we see that growth is the average rate of change in sales, while the trend line above shows that trend shows the steady movement of sales.