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 117.50% per annum.
- MSFT price at the close of July 11, 2025 was $503.32 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 49.98% per annum.
- MSFT price at the close of July 11, 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 MSFT 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: May 2, 2025
End date: July 11, 2025
a = 2.3417
b = 0.0021
s = 0.0084
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 117.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0084) – 1
= 3.40%
May 2, 2025 calculations
Top border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 + 2 × s)
= Exp(a + b × 1,754 + 2 × s)
= Exp(2.3417 + 0.0021 × 1,754 + 2 × 0.0084)
= Exp(6.0923)
= $442.45
Bottom border of price channel:
Exp(Y1,208)
= Exp(a + b × X1,208 – 2 × s)
= Exp(a + b × 1,754 – 2 × s)
= Exp(2.3417 + 0.0021 × 1,754 – 2 × 0.0084)
= Exp(6.0589)
= $427.90
July 11, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.3417 + 0.0021 × 1,824 + 2 × 0.0084)
= Exp(6.2414)
= $513.55
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.3417 + 0.0021 × 1,824 – 2 × 0.0084)
= Exp(6.2079)
= $496.66
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 117.50% per annum.
- MSFT price at the close of July 11, 2025 was $503.32 and was inside the primary price channel.
Secondary Trend
Start date: June 24, 2025
End date: July 11, 2025
a = 4.1918
b = 0.0011
s = 0.0062
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 49.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0062) – 1
= 2.52%
June 24, 2025 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,807 + 2 × s)
= Exp(4.1918 + 0.0011 × 1,807 + 2 × 0.0062)
= Exp(6.2110)
= $498.21
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,807 – 2 × s)
= Exp(4.1918 + 0.0011 × 1,807 – 2 × 0.0062)
= Exp(6.1861)
= $485.96
July 11, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.1918 + 0.0011 × 1,824 + 2 × 0.0062)
= Exp(6.2299)
= $507.71
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.1918 + 0.0011 × 1,824 – 2 × 0.0062)
= Exp(6.2050)
= $495.22
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 49.98% per annum.
- MSFT price at the close of July 11, 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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