SAFE TOOLBOXES^{®} comes with the following forecast models:
#  Forecast Model 

1 
ARIMA (Autoregressive integrated moving average model) 
2 
AR (Autoregressive model) 
3 
MA (Moving average model) 
4 
GARCH (Generalized Autoregressive Conditional Heteroskedasticity model) 
5 
HoltWinters Additive 
6 
HoltWinters Multiplicative 
7 
HoltWinter Exponential Smoothing 
8 
Last value 
9 
Historical mean 
10 
Moving average 
11 
Linear time tendency 
12 
Quadratic time tendency 
13 
Cubic time tendency 
Regression models can also be used for forecasting purposes. This can be done separating one part of your data to represent the “past” and another part of your data to represent the “future”. This method may be useful if the explanatory variables are known in advance or if they are easier to predicted than the dependent variable itself. In this approach only the “past” portion of your data is used to fit the parameters of the regression model.
Consider the following time series:
A 
B 
C 

1 
Sample database 


2 



3 
Time 
Value 

4 
1 
103.2 

5 
2 
106.6 

6 
3 
106.6 

7 
4 
106.6 

8 
5 
106.6 

9 
6 
106.6 

10 
7 
108.5 

11 
8 
111.7 

12 
9 
116.2 

13 
10 
117.4 

14 
11 
119.2 

15 
12 
121.0 

16 
13 
122.5 

17 
14 
124.2 

18 
15 
119.1 

19 
16 
117.0 

20 
17 
114.0 

21 
18 
109.0 

22 
19 
107.0 

23 
20 
104.0 

24 
21 
98.2 

25 
22 
93.5 

26 
23 
88.7 

27 
24 
83.9 

28 
25 
80.7 

29 
26 
78.5 

30 
27 
73.9 

31 
28 
72.3 

32 
29 
71.4 

33 
30 
71.6 

34 
31 
71.1 

35 
32 
71.2 

36 
33 
71.5 

37 
34 
72.6 

38 
35 
74.2 

39 
36 
79.0 

40 
37 
82.3 

41 
38 
84.5 

42 
39 
89.0 

43 
40 
92.5 

44 
41 
94.5 

45 
42 
99.0 

46 
43 
101.7 

47 
44 
104.3 

48 
45 
106.5 

49 
46 
108.7 

50 
47 
109.0 

51 
48 
109.0 

52 
49 
109.0 

53 
50 
109.0 

54 



To forecast a value for dates 51 to 55 of this series using an AR(1) model just follow the steps below:
Now, the results will appear at the bottom of the Econometrics Toolbox tab.
A first check of the goodness of fit of our model can be done by inspecting the line plot chart. A good fit will put the red line (predicted values) near to the blue line (actual values). The dotted line represents the out of sample prediction of our model.
The equation of our AR(1) model is placed in the tab. This table shows the fitted parameters and useful statistics of our model. Not all forecasting models have a representation in the equation tab. This is the case, for instance, for the HoltWinters models or the moving average model.
You can run different specification for your ARIMA model or use other forecast methodologies. The “Historical results” tab will keep the main statistics of your models. Particularly, in the case of forecasting models, is a good practice to reserve some portion of your data to run out of sample tests. By doing this, the forecast statistics: MAD (mean absolute deviation), MAPE (mean absolute percent error) and RMSE (root of mean square error) available in this tab can help you to rank your models.