Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 8.25% per annum.
- MCD price at the close of March 26, 2025 was $313.58 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 27.39% per annum.
- MCD price at the close of March 26, 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 MCD 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: April 6, 2021
End date: February 7, 2025
a = 5.2992
b = 0.0002
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 8.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.39%
April 6, 2021 calculations
Top border of price channel:
Exp(Y257)
= Exp(a + b × X257 + 2 × s)
= Exp(a + b × 375 + 2 × s)
= Exp(5.2992 + 0.0002 × 375 + 2 × 0.0505)
= Exp(5.4816)
= $240.24
Bottom border of price channel:
Exp(Y257)
= Exp(a + b × X257 – 2 × s)
= Exp(a + b × 375 – 2 × s)
= Exp(5.2992 + 0.0002 × 375 – 2 × 0.0505)
= Exp(5.2796)
= $196.29
February 7, 2025 calculations
Top border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 + 2 × s)
= Exp(a + b × 1,778 + 2 × s)
= Exp(5.2992 + 0.0002 × 1,778 + 2 × 0.0505)
= Exp(5.7862)
= $325.78
Bottom border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 – 2 × s)
= Exp(a + b × 1,778 – 2 × s)
= Exp(5.2992 + 0.0002 × 1,778 – 2 × 0.0505)
= Exp(5.5842)
= $266.18
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 8.25% per annum.
- MCD price at the close of March 26, 2025 was $313.58 and was inside the primary price channel.
Secondary Trend
Start date: May 20, 2024
End date: March 26, 2025
a = 4.5356
b = 0.0007
s = 0.0433
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 27.39%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0433) – 1
= 18.89%
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,515 + 2 × s)
= Exp(4.5356 + 0.0007 × 1,515 + 2 × 0.0433)
= Exp(5.6268)
= $277.77
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,515 – 2 × s)
= Exp(4.5356 + 0.0007 × 1,515 – 2 × 0.0433)
= Exp(5.4537)
= $233.63
March 26, 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(4.5356 + 0.0007 × 1,825 + 2 × 0.0433)
= Exp(5.8324)
= $341.16
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.5356 + 0.0007 × 1,825 – 2 × 0.0433)
= Exp(5.6593)
= $286.95
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 27.39% per annum.
- MCD price at the close of March 26, 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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