Emre Eryilmaz Forecasting Project

8/14/2019 Emre Eryilmaz Forecasting Project

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Part A: FORECASTNG REAL WORLD DATA

In this part, time series forecasting methods are used. Basically, time series

forecasting is a time ordered sequence of datasets taken at regular intervals. Datasets given

daily values of closing prices of Intel, Microsoft and General Electrics in the range between

7/11/1999 and 11/12/1999 that includes 89 days. For every material, 7 time series forecasting

methods are applied that are Naive Method, Moving Average Method, Weighted Moving

Average Method, Exponential Smoothing, Holts Exponential Smoothing, Linear Regression

and Winters Exponential Smoothing Method. Also, relation between the forecasted values

and actual values are compared in the line graph. After the observations and analysis, RMSE,

MSE, MAD and MAPE error measuring techniques applied to datas to determine the better

time series forecasting method. For the first company Intel , there is short explanations

about the forecasting method which is applied and there is snapshots from MS Excel to show

readers the components of formulas and help them to understand how methods are applied to

datasets. Also, there is an appendix part at the end of the project that includes detailed

explanations of methods.

These procedeures are valid for all forecast of these project.

- All last 20 days assumed as unknown and fillid with turquaze color.

- Because of last 20 days assumed unknown, the actual values that we need to calculete

next forecasted values calculated by using previous forecasting values. For example,

F(t-1) values used as an actual value A(t) to calculate F(t+1).

- MSE = mean square error

RMSE = root mean square error

MAD= mean absolute deviation

MAPE= mean absolute percent error

A(t)= actual value at time t

F(t)= forecasted value at time t

1.1 Intel

1.1.1. Naive Forecast

Ens 208, Fall 2006 Project 01Emre Erylmaz

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Naive Method is simple but widely used in many areas. This method uses single previous

value of a time series as the basis of the forecast. See Appendix A for details.

Figure 1. Naive Method Forecasting

We forecasted the first day of the 20 days by using actual values and than we calculated the

19th day by using th first forecasted value as an actual value of that time.


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Figure 2. Error determination in Naive Method

The graph of Naive Method is;

Figure 3. Actual vs. Forecasting

1.1.2. Moving Average Method,


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One of the advantage of moving avarage method is that you can use

historical data by using period of time. In this method we will calculate the

value of the next period by taking avarage value of the previous N actual

values. One can use Average or Sum/Count commands to calculate

avarage value. See Appendix B for details.

1.1.2.1. Moving Average Method, N=69;

We used different N values to understand how the period of the time affects

the accuracy of the forecasting. First take N equal to 69 to understand how a

long period of time determines the accuracy of the forecasting. And then we

took smaller range to show the difference between big ranges and small

ranges.

Figure 4. Calculation of Moving Average with N=69


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Figure 5. Error calculation

Figure 6. Actual vs. Forecasting, N=69


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1.1.2.2. Moving Average Method, N= 20;

Figure 7. Calculation og forecasting, N=20


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Figure 8. Error calculation, N=20



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1.1.2.3.Moving Average Method, N=10;

Figure 10. Calculation of forecasting, N=10


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1.1.2.4. Moving Average Method, N=5;


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Figure 13. Forecast Calculation, N=5



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For Intel, in moving avarage method, when we decrease the N value as it seen generally

RMSE, MSE, MAD, MAPE values increases. When N=69, we have smalest and when N=5,

we have the largest error. This situation may stem from weekly closing prices may change but

if we look at overall closing prices, it is more closer to actual values.

1.1.3 Weighted Moving Average

In this method, forecast made by multiplying every character with a weight constant with te

previous values and taking the sum of these values. See Appendix C for details.


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Figure 16. Calculation of Forecast

a,b,c,d and e values are found by minimizing RMSE value of the first 69 days by using solver.

The value of RMSE in the picture is minimized. In the solver scene constrains are the a,b,c,d,e

and t values that are the weight constant that are found by using Solver.


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Figure 17. Using Solver in Weighted Moving Average

The RMSE and other error values are for the last 20 days.


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Figure 18. Eror calculation

Figure 19. Actual vs. Error1.1.4. Exponential Smoothing

Alpha constant s used in this method to be able to calculate better forecasting values. Alpha is

found by using Solver. See Appendix D for details.


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Figure 20. Using Solver in Expo. Smoothing



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Figure 22. Actual vs. Forecast

1.1.5. Holts Exponential Smoothing

In this method, forecast is calculated by using 2 different components that are smoothed

forecasting F(t) and trend estimateT(t). F(t) and T(t) both includes smothing constants alphaand beta. These two constants are used while calculating F(T) and T(t). See appendix E for

details.

Constants are calculated by using Solver according to last 69 days.


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Figure 23. Calculatin alpha by using Solver

Figure24. Error Calculation


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Figure 24. Actual vs. Forecasting

1.1.6. Linear Regression

Linear regression method based on the slope of the actual values because of time. Slope is

represented by b. There is a slope function in excel, so we can fin easily the slope of the

datas.

Date order(1st column)

Actual values (3rd column)


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b= Slope(C28:C96;A28:A96)

Figure 25. Calculation of Slope

a represents the intersection point of y axis and the x axis where x =0. Intersept command

is very useful to find a value in Excel.

Figure 26. Calculation of Intercept


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Figure 27. Error and Forecast Calculation

Figure 27. Actual vs. Forecasting1.1.7 Winters Exponential Smoothing

In this method there is additional seasonality(St) factor affects the calculation of forecasts. For

seasonality, there is also a smoohing constant that is gamma besides alpha and beta constans

of F(t) and T(t).


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Similarly alpha and beta, gamma constant is also in the range of 0 and 1. Because of the

seasonality factor in winters method, it provides better forecasting values. So, the sensivity

for seasonal chances is higher than the other methods. The formula of seoanality is;

S(t+1)= A(t)/F(t)+(1-)S(t-p) is gamma and p is the period.

First S(t) values found by taking avarage of theactual values that period divided by actual

value at time t. Period is 5 and because of datas we have weekly values without weekends we

take p=5.

Figure 28. Calculation of SeasonalityTrend is also component of Winters method. The trend formula is;

T(t)=*(F(t+1)-F(t))+(1-)*T(t)


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Figure 29. Calculation of Trend

F(t)= *A(t)/S(t-p)+(1- )*(F(t)-A(t)) and W(t+m)=(F(t)+m*T(t)*S(t+m-p)

Figure 30. Determination of constants and calculation of F(t) and W(t)

Figure 31. Error determination


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The best model for Intel is Moving Average Method with N=69. It is a little surprising

because there is more complicated methods give bigger RMSE. If we look at the forecast and

actual values of Mov. Aver. N=69, we see that values are increasing or decreasing similarly.

And if we look at the graph We. Mov. line is close to avarage of last 20 days values. That alsomay be the reason of weighted moving averages values closer to actual values than other

methods. Also, because of there is no sharp decreases or increases in actual values, avarage

values are similar to these values. That is also another reason that moving average method

give better values than Winters exponential smoothing.

1.2. Microsoft

1.2.1 Naive Method


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Figure 33. Calcution of Forecast

Figure 34. Calculation of Errors


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1.2.1 Moving Average Method

1.2.1.1 N=69


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1.2.1.2. N=20


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Figure 39. Forecast vs. Actual

1.2.1.3. N=10


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1.2.1.4. N=5



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Figure 43. Forecast vs. Actual

The best two N value is N=69 and N=5 and worsts are N=20 and N=10. The reason that 69 isthe best one may be increase and decrease in the actual values keeps it in long term close to

stable. The reason 5 is the second best value is may it adjust itself to short terms decrease and

increase. N= 10, 69 do not adjust itself so they have bigger RMSE.

1.2.2. Weighted Moving Average


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Figure 44. Forecast and Error Calculation

Figure 45. Actual vs Forecast

1.2.3 Exponential Smoothing


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Figure 47. Actual vs Forecast1.2.4. Holts Exponential Smoothing


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1.2.5 Linear Regression


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1.2.6. Winters Exponential Smoothing


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For Microsoft, Moving Average, N=69 is the best model according to RMSE. If we look at the

graph actual value and forecast for N=69, it is seen that forecast values are very close to

middle of decrease and increase of the actual values. For this reason RMSE is small. The

worst on is Naive Method, because it uses only the previous t, it could not adjust itself to


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differences. If we compare Microsoft with Intel, it may seen that generally models fits better

to Microsoft actual calues.

1.3 General Electric

1.3.1. Naive Method

Figure 54. Error Calculation


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1.3.2 Movin Average

1.3.2.1. N=69


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1.3.2.2. N=20




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1.3.2.3. N=10



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1.3.2.4. N=5


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Figure 63. Actual vs ForecastThe best N values are N=20 and N=10. The worst one is N=69. Because of there is an

increase in the actual values of G.E., mov. avererage used previous lower level values, so

RMSE is high. Also, sensivity is important here and mov. average and naive cannot adjust


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itself. Unlike Intel and Microsoft, the actual values of G.E. changes more sharply. So,

sensivity becomes important.

1.3.3. Weighted Moving Average




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1.3.4. Exponential Smoothing



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1.3.5. Holts Exponential Smoothing


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1.3.6. Linear Regression

Figure 70 Forecast and Error Calculation


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Figure 71 Actual vs Forecast

1.3.7. Winters Exponential Smoothing

Figure 72 Forecast and Error Calculation


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Figure 73 Actual vs Forecast Although we expect winter will fit the best, we get the lowest RMSE by the Lineer Regression method. The worst model is again Naive Method. Mov. Average method with N=5

is the second and also good relatively to other methods. The reason that Linear Regression fit

the best is that it adjust itself the increase in the actual values and at the end of 20 days it give

the lowest RMSE.

As a conclusion of this part;

- Moving Average Method is the most suitable model for Intel and Microsoft.

- Naive method provide bad results.

- Winter method is not the most suitable but it provided good forecasting values because

of its seasonality and can consider sharp increases and decreases.

- Generally, Winter and Holts methods provide similar forecasting values.

2. Seasonality

Seasonality is basically repeating movements in series. If there is similarity of seasonality

graphics of different materials, it can be said that these materials effects each other. So,

seasonality graphics gives us the idea of there is a relationship between the seanalities or there

is not a relationship. In this section we will look at the seasonality graphics of Intel, Microsoft


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and G.E. to understand is there a relationship between these firms. The values are taken from

the winters seasonality (St) calculation.

Figure 74. Seasonality Graph

It is easily seen in figure 74 that the seasenality values are not exactly same but the behaviour

of the firms is very identical. Especially, G. E. And Microsoft shows very similar behaviour. If

we look at the peaks and valleys of these 2 firm they are at the same date. Because of the

seasonality reapets itself we should look only one period that consists 5 days.


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Figure 75. Seasonality graph of 5 days

As mentioned before, values are not identical but increase and decrease times are identical. If

one increase or decrease the other one too. So, we can say there is a relationship between

these firms.

We should look at production graphs to see the relationship of these firms.


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Figure 76. Production Graph

As it is seen in the figure 76, level of production of the firms are different but if we look at the

lines behaviours G.E. and Microsoft is very similar and Intel and other two firms is similar

but not much as the relation between G.E. and Microsoft.

3. Control Charts

Control charts can be use to test the suitability of the forecasting methods that applied to

firms.

3.1. Naive Forecast Intel


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Figure 77. Data that will be used in control chart


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Figure 78. Control Chart

RMSE value of Naive method is 1,98 according to first 69 days. But the last 20 days forecast

do not fit in the UCL and LCL because of unsuitable values of naive forecast. Only the first

two values fit in the chart and other 18 do not. As it seen in figure 78, for the last 18 value

error amount is higly increasing. So, it can be said that Naive Method is not a good method to

forecast.

3.2.1 Moving Average, N=20


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Figure 79. Data that will be used in control chart Figure

Figure 80. Control ChartThe borders of control limits are extensive and forecast values is suitable to it. So, it can be

said that moving average is a good method with N=20.


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3.2.2 Moving Average, N=10




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It is seen that there is 3 dots outside the limits when the changes are relatively high. But 17

dots is in the borders so, it can be said that N=10 provide quite well but not much as N=20.

3.2.3. N=5



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All the dots are in the borders, so it can be said that moving average with N=5 is doing well.

3.3. Weighted moving Average


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All the dots are between the range of control bars, so it can be said that weighted moving

average is suitable to forecast.

3.4. Exponential Smoothing


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All dots values are between upper and lower controls limits so, we can say exponential

smoothing is doing well.

3.5. Holts Exponential Smoothing


Figure90. Control Chart


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LCL


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All dots calculated by exponential smoothing are in the range of control limits. So, we can say

exponential smoothing doing well with Intel values.

3.7. Linear Regression



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Figure92. Control Chart

As it seen in figure 92 only one value is outside from the control levels. All values are

negative so, we understand that linear regression forecasted less than actual values of Intel.

3.8. Winters Exponential Smoothing


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As it seen in the figure 94, 11 dots are outside the range of upper and lower limits. And these

values are generally bigger values than UCL. So, it can be said that winter could not adjust

itself t forecast bigger actual values.


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3.9. General Observations

- Because of there is no big sharp changes in the actual values Moving average and

weighted moving average forecasted well.

- There is a seasonality in a period of weeks but the values are close to each other.

...

4. Correlation

4.1. General Information About the Graphs

Correlation and r^2 values used are used to detect correlation. The relation between firms is

correlation. Namely, we will determine is there relationship between firms or not.

Correlation graphs show the relationship between firms. CORREL( ; ) formula is useful to

find correlation value in Excel. In graphs there is are two values of y. First one is actual

value and the second one is found by using x. If y values are closer to each other, it can be

said that change in x cause some changes in y and we can say there are correlated. r^2 value is

also determined by RSQ( ; ) command in Excel.

Second type of graph is the production graph . It has two different closing values in y axis ad

time scale in x axis. Because of this, it helps us examining is there a decrease or increase

follow one firm to another. Is this provide us to understand the relation between two firms.

4.2. Intel Microsoft Correlation


Correlation r^20,211709 0,044821

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Figure 94. Correlation graph of Intel and Microsoft

Figure 95. Correlation graph of Microsoft and Intel


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As it seen in the graphs there is no strong relationship between Microsoft and Intel. So it can

not be said that an increase in Microsoft do not directly cause an increase in Intel and vice

versa. As it seen in the graph the correlation between them is very low that is 0,211709 that

means there is no real relationship between them. Even if there is iit is really weak. And r^2

value is 0,044831 which is very far away from 1. It means there is almost %4 relationship

between these firms. To sum up, according to these values it can be said that there is not a real

correlation between these two firm.

Figure 96. Production graph of Microsoft and IntelAs it seen in the production graph there is no strong correlation. For example, in the rectangle

The value of microsoft decreasing and Intel is increasing. To sum up, if you look deeply in

graps, it will be seen that there is no strong correlation between the actual values of these

firms.

4.3. Intel G.E. CorrelationCorrelation r^2

0,22276 0,049622


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Figure 97. Correlation graph of Intel and G.E.

Figure 98. Correlation graph of G.E and Intel

As seen in the graphs there is no strong relationship between two firms according to data we

have examined. Increase or decrease in the value of one firm do not affect the other one


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directly. The reasons we said for the correlation between Intel and Microsoft is the same in

here.

Figure 99. Production graph of G.E. and Intel

If we look at production function we can easily say there is no strong relationship between

Intel and G.E. In the rectangle The actual values of G.E. increasing and Intels atual values are

decreasing. Also there is no paralel vlues except from the beginning and end of the graph.

Moreover, correlation value is 0,22276 that means there is no strong relationship and r^2 is

0,049622 that means %4 they are correlated.

To sum up it can easily said thre is no real correlation between Intel and G.E. according to

graphs and values.

4.4 Microsoft and G.E. Correlation


Correlation r^2

0,818482 0,669913

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Figure 100. Correlation between Microsoft and G.E.

Figure 101. Correlation between G.E. and Microsoft

If we look at the values of the two graphs detailly, it is obviously seen there is a correlation

between these two firms. The values of the firms increasing and decreasing paralelly. We can

say that if one of the value of one firm decrease or increase, the othar one will ce affected

paralelly and its values will decrease or increase according to other firm. Also, correlatian and


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r^2 values illustrase this technically. The correlation value is 0,818482 which shows there is a

high correlation between these two firms. Also r^2 is 0,669913 that means these firms are

almost %65 correlated.

Figure 102. Production graph of G.E. and Intel

If you look at the figure 102, it is easily seen that two firms values are behaving almost parallel. For example if you look at purple rectangular, you see that one of the firms actual

values increasing and the other one too. Also, if you look at blue rectangular two firms

actualvalues are decreasing. Becasuse of the correlation is not %100 percent, there is also

some points that seem do not correlate such as the at the end of the time but we found that

these firms are almost %65 correlated which is a high correlation ratio.

4.6. Conclusion

It was shown that there is a strong correlation between G. E. and Microsoft. The reason might

be that Microsoft higly uses G. E. products and these affects its closing prices accordin to

G.E. . The opposite situation is also possible. The value of correlation is 0,818482 and r^2 is

0,669913 that illustrates the relationship.

Surprisingly there is no high correlation between Intel and microsoft although they are both

computer technology areas and the owner of the two firm is Bill Gates. We expected that


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microsoft and intel will be highly correlated but it was not. The correlation value is 0,044831

and r^2 value is 0,211709 that is very small to become correlated.

PART B: SURVEY OF FORECASTING WITH NEURAL NETWORKS3. Neural network ProductsTo forecast better and to became more close to actual values, lots of software companies are

trying to produce a neural network forecasting products. In my search i tried to some neural

network forecasting products. These are NeuroSolutions5, Alyuda Forecaster, Neural Power,

Easy NN Plus, Forecaster XL, Trading Solutions and Tiberius XL.

I have chosen Alyuda forecaster and Easy NN Plus forecaster.

4.Program TutorialAlyuda forecaster is a demo version and it does not allow you to forecast your datas. In the

program they are examples that how Alyuda forecasts.

Lets do an example.

After clicked on shortcut of the program a window opens.


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Then it asks to select mode.


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There is demo examples that is seen in the picture below.

We chosed Sales Forecasting to see how it calculates business application.


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If you want it also shows the details...


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The other product is Easy NN but when i used it it provide bad results. So i did not putit.

Appendix AMain resource of Naive Method is the previous forecasted value and previous actual value.

The difference between the previous A(t) and A(t-1) real values and sum of the result with

A(t). The general formula of Naive Method is F(t+1) = A(t) + (A(t)-A(t-1)). Althoug

the method is simple, the method is useful for stable series.

Appendix B

F(t+1)=(A(t)+A(t-1)+A(t-2)....+A(t-N))/N

N is the number of values that we used in forecasting

Appendix CFirtly value of N determined. Weight contstant have to be between 0 and 1. Also sum of the

weight contstants have to be 1. weights can be denoted with w1, w2, ..wn or a, b, c...n.


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Formula is F(t)= w1*A(t-n)+w2*A(t-(n-1))+...+wn*(At-1)

*Firstly, previous actual value is multiplyed.

Appendix DIn this method a constant is used to forecast better. Constant has t be between 0 and 1. the

formula is: F(t)=F(t-1)+(A(t-1)-F(t-1)

Appendix EHere is T(t) values to put trend in forecasting.

F(t+1)= A(t)+(1-)(F(t)-T(t))

T(t+1)=(F(t+1)-F(t))+(1- )T(t)

H(t+m)=F(t+1)+T(t+1)

References:Yahoo Finance (2006) Stock Research Center / Histrocial Quotes. http://biz.yahoo.com/r/ .

Accessed on November 8, 2006.
http://biz.yahoo.com/r/http://biz.yahoo.com/r/

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Emre Eryilmaz Forecasting Project