There are theoretical models that are used to predict stationary and transforming effects. In this essay, ARIMA and autocorrelation models shall be discussed.
ARIMA with a single feature of direction and magnitude is a predicting method that estimates the expectations of values of a sequence depending fully in its inactivity. It is often used where there is a small duration of predicting that needs a minimum of forty chronological facts and figures. The application of ARIMA is greatest where the data shows a constant and steady outline over a period during which the outliers is the least.
ARIMA is also referred to as Bos-Jenkins in honor of its’ initial writers (Broersen, pp 33). It is the most advanced method compared to exponential smoothing methods especially when the figure collected is convincingly extensive and the connection involving the earlier observations is steady. Smoothing method is more appropriate if the collected facts are small and extremely unpredictable. This is done especially if you have at least 38 collected facts.
When using ARIMA method, firstly ensure that the sequence becomes steady for a period time. A drift in economies and businesses means that the data is not stationary. The numbers should also exhibit some general instability over a period. This occurs in a sequence that is recurrent and the rate of growth is high. If the stationarity circumstances are not achieved, then computation linked to such a procedure cannot be done.
Another Feature in ARIMA is differencing. This is done when the data depicts a non stationarity. This is the best method of changing a non stationary series to a stationary series. The operation involves getting the difference between the existing periods from the earlier one. If the change is effected in a one way process, then it is said to have been first differenced (Broersen, pp 47).
This process gets rid of a stable rate. However, if the rate is appreciating at a very high rate then the shame process can be performed and do the differencing for the second time. This kind of data shall be become second differenced.
These are mathematical values that shoe how collected facts that show how a sequence is associated to that series over a period of time. It’s a measure of how specific spaced out data values at said number of times are correlated to one another over time (Miller pp 8). The spaced out period is known as lag.
Lag 1 shows how values 1 period are spaced. Autocorrelation at lg 2 determines how two collected figures which are spaced out in 2 periods are correlated in a sequence. These measures are usually done graphically. The plots are known as correlagrams where by the values different correlation values are done at different lag periods. It is called autocorrelation function and is imperative in ARIMA technique.
There are various causes of auto correlation. One of it is spacial autocorrelation which occurs when two errors are connected either specially or geographically or both. This can be corrected by giving time to adjust as in Macro sequence of data. For example if the US interest rates then there would be a connected change in other countries.
Therefore, attaining balance shall take time. It can also occur when influences prolong, for example, if the US rates is expected to rise, then there shall be a linked change in other countries until the US shall announce the balance. It can also caused by interfering with data in order to suit the needs of the statistician. Finally, it can be caused by wrong specification (Miller, pp 13).
This happens when the variables are ignored. The omitted values will cause general disturbance in the plots of the curve that shall resemble ?t = ?2X2 + ut when the right equation is Yt = ?0 + ?1X1 + ?2X2 + ut. The possible geneses of such a problem are omission of variables, wrong specification of the functions and when the errors are not random.
The solutions to autocorrelation include identifying its cause, increasing the number of circumstances and making right specifications. Other solutions include use of microfit which shows the process. It should be noted that confusion can easily arise between misspecified dynamics and serial correlation. Its therefore recommended to begin with general dynamic then try to solve the application of test correlation. The AR1 is the only model that can be done in dynamic model
Both ARIMA and autocorrelation are models that can be effectively used by economists to explain the change and transformation or stationarity of an observation.
Broersen, Thomas. Autocorrelation and spectral analysis. Springer, 2006: pp 30-50
Miller, Frank. Autocorrelation. VDM ltd, 2010: pp 1-20