Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.20% per annum.
- PEP price at the close of April 21, 2025 was $141.73 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 24.42% per annum.
- PEP price at the close of April 21, 2025 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PEP price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 24, 2022
End date: April 21, 2025
a = 5.2597
b = -0.0001
s = 0.0465
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0465) – 1
= 20.43%
October 24, 2022 calculations
Top border of price channel:
Exp(Y632)
= Exp(a + b × X632 + 2 × s)
= Exp(a + b × 915 + 2 × s)
= Exp(5.2597 + -0.0001 × 915 + 2 × 0.0465)
= Exp(5.2452)
= $189.65
Bottom border of price channel:
Exp(Y632)
= Exp(a + b × X632 – 2 × s)
= Exp(a + b × 915 – 2 × s)
= Exp(5.2597 + -0.0001 × 915 – 2 × 0.0465)
= Exp(5.0593)
= $157.48
April 21, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.2597 + -0.0001 × 1,825 + 2 × 0.0465)
= Exp(5.1383)
= $170.43
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.2597 + -0.0001 × 1,825 – 2 × 0.0465)
= Exp(4.9524)
= $141.52
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.20% per annum.
- PEP price at the close of April 21, 2025 was $141.73 and was inside the primary price channel.
Secondary Trend
Start date: July 26, 2024
End date: April 21, 2025
a = 6.3559
b = -0.0008
s = 0.0298
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -24.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0298) – 1
= 12.67%
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,072)
= Exp(a + b × X1,072 + 2 × s)
= Exp(a + b × 1,556 + 2 × s)
= Exp(6.3559 + -0.0008 × 1,556 + 2 × 0.0298)
= Exp(5.2222)
= $185.34
Bottom border of price channel:
Exp(Y1,072)
= Exp(a + b × X1,072 – 2 × s)
= Exp(a + b × 1,556 – 2 × s)
= Exp(6.3559 + -0.0008 × 1,556 – 2 × 0.0298)
= Exp(5.1029)
= $164.50
April 21, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(6.3559 + -0.0008 × 1,825 + 2 × 0.0298)
= Exp(5.0159)
= $150.79
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.3559 + -0.0008 × 1,825 – 2 × 0.0298)
= Exp(4.8966)
= $133.83
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 24.42% per annum.
- PEP price at the close of April 21, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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