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 113.34% per annum.
- MSFT price at the close of July 31, 2025 was $533.50 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 56.77% per annum.
- MSFT price at the close of July 31, 2025 was higher than the top border of the secondary price channel by $12.81 (2.46%).
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 21, 2025
a = 2.4793
b = 0.0021
s = 0.0082
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 113.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0082) – 1
= 3.34%
May 2, 2025 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,733 + 2 × s)
= Exp(2.4793 + 0.0021 × 1,733 + 2 × 0.0082)
= Exp(6.0933)
= $442.89
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,733 – 2 × s)
= Exp(2.4793 + 0.0021 × 1,733 – 2 × 0.0082)
= Exp(6.0605)
= $428.60
July 21, 2025 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,813 + 2 × s)
= Exp(2.4793 + 0.0021 × 1,813 + 2 × 0.0082)
= Exp(6.2594)
= $522.91
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,813 – 2 × s)
= Exp(2.4793 + 0.0021 × 1,813 – 2 × 0.0082)
= Exp(6.2266)
= $506.03
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 113.34% per annum.
- MSFT price at the close of July 31, 2025 was $533.50 and was inside the primary price channel.
Secondary Trend
Start date: June 24, 2025
End date: July 30, 2025
a = 3.9980
b = 0.0012
s = 0.0057
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 56.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0057) – 1
= 2.31%
June 24, 2025 calculations
Top border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 + 2 × s)
= Exp(a + b × 1,786 + 2 × s)
= Exp(3.9980 + 0.0012 × 1,786 + 2 × 0.0057)
= Exp(6.2096)
= $497.49
Bottom border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 – 2 × s)
= Exp(a + b × 1,786 – 2 × s)
= Exp(3.9980 + 0.0012 × 1,786 – 2 × 0.0057)
= Exp(6.1868)
= $486.27
July 30, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(3.9980 + 0.0012 × 1,822 + 2 × 0.0057)
= Exp(6.2539)
= $520.05
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(3.9980 + 0.0012 × 1,822 – 2 × 0.0057)
= Exp(6.2311)
= $508.32
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 56.77% per annum.
- MSFT price at the close of July 31, 2025 was higher than the top border of the secondary price channel by $12.81 (2.46%).
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
Check out MSFT and 1,499 other stocks on our new website