# Trend Analysis and Isolating the Cyclical

```Trend Analysis and Isolating the Cyclical Component of Intel Stock,
January 2005 – December 2009
Andrew Brown
Stats 350
Managerial Report #7
Due: 4/28/10
I am comparing a linear model and a polynomial model to find which one best fits Intel’s
stock prices as a modeling trend. I will then use the best fitting trend line to determine whether
or not a cyclical component exists in my time series. Equation 1 shows the proposed linear
model used for estimation.
Yt = β0 + β1t + εt
(1)
Equation 2 shows the proposed polynomial model used for estimation.
Yt = β0 + β1t + β2t2 + εt
(2)
Table 1 shows the results I obtained when I ran both the linear and polynomial model for trend.
Table 1. Regression Results for Modeling Trends
Dependent Variable: Adjusted Close Stock Price (\$)
Constant
Time
Time2
R2
F
Standard Error
Observations
Linear Model
21.72*
(0.000)
-0.072*
(0.001)
Polynomial
Model
21.33*
(0.000)
-0.034
(0.702)
n/a
n/a
-0.001
(0.658)
0.161
11.161
2.872
60
0.164
5.603
2.892
60
* denotes significance at the 5% significance level
(p-value)
For the linear model, time is significant in explaining Intel’s stock price at the 5%
significance level. For the polynomial model, neither time nor time squared is significant in
explaining Intel’s stock price at the 5% significance level. The coefficient of determination in
both models is roughly equal as only 16% of the variability in stock price is explained by time.
However, the linear model is the best fit because it has a lower standard error, meaning there is
less variance in its residuals, and also for the reason that time is significant in explaining stock
prices at the 5% significance level in this model.
Using the trend line from the linear model, I calculated the percentage of trend over time.
For this series, I obtained Graph 1 from the data.
Graph 1. Percentage of Trend
140
120
100
Percentage of
Trend
80
60
40
20
0
0
10
20
30
40
50
60
70
Time (January 2005 - December 2009)
From the data obtained from the linear model and the percentage of trend shown in Graph
1, there does not seem to be any evidence of a cycle in my series. I concluded from the lack of
equal clusters of data points alternating above and below the percentage of trend line that no
discernable cycle exists.
```