Question

Explain why a typical linear regression model can’t be used for time series analysis and describe an example of a time series

Answer 1

A. Of course you can use linear
regression with time series data as long as:
1. The inclusion of lagged terms as regressors
does not create a collinearity problem.
2. Both the regressors and the explained variable
are stationary
3. Your errors are not correlated with each other
4. The other linear regression assumptions apply
No autocorrelation is the single most important
assumption in linear regression. If autocorrelation is
present the consequences are the following:
1. Bias: Your "best fit line” will likely be way off
because it will be pulled away from the “true
line" by the effect of the lagged errors.
2. Inconsistency: Given the above, your sample
estimators are unlikely to converge to the
population parameters.
3. Inefficiency: While it is theoretically possible,
your residuals are unlikely to be homoskedastic
if they are autocorrelated. Thus, your confidence
intervals and your hypothesis tests will be
unreliable.

In conclusion, if you are trying to use the model to predict sales, I'm not sure it is useful, even as a "simplistic” model
You may want to use an auto regressive model instead. It has the advantage of likely fitting your data much better than a straight line and you are more likely to reliably link present sales to past sales than just the passage of time.

B. A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

Time series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements.

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