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 0.08% per annum.
- MSFT price at the close of March 27, 2025 was $390.58 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.80% per annum.
- MSFT price at the close of March 27, 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: January 25, 2024
End date: March 27, 2025
a = 6.0385
b = 0.0000
s = 0.0400
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0400) – 1
= 17.33%
January 25, 2024 calculations
Top border of price channel:
Exp(Y962)
= Exp(a + b × X962 + 2 × s)
= Exp(a + b × 1,396 + 2 × s)
= Exp(6.0385 + 0.0000 × 1,396 + 2 × 0.0400)
= Exp(6.1152)
= $452.68
Bottom border of price channel:
Exp(Y962)
= Exp(a + b × X962 – 2 × s)
= Exp(a + b × 1,396 – 2 × s)
= Exp(6.0385 + 0.0000 × 1,396 – 2 × 0.0400)
= Exp(5.9553)
= $385.80
March 27, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.0385 + 0.0000 × 1,823 + 2 × 0.0400)
= Exp(6.1142)
= $452.23
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.0385 + 0.0000 × 1,823 – 2 × 0.0400)
= Exp(5.9543)
= $385.42
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.08% per annum.
- MSFT price at the close of March 27, 2025 was $390.58 and was inside the primary price channel.
Secondary Trend
Start date: December 4, 2024
End date: March 27, 2025
a = 8.4076
b = -0.0013
s = 0.0224
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -38.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0224) – 1
= 9.37%
December 4, 2024 calculations
Top border of price channel:
Exp(Y1,179)
= Exp(a + b × X1,179 + 2 × s)
= Exp(a + b × 1,710 + 2 × s)
= Exp(8.4076 + -0.0013 × 1,710 + 2 × 0.0224)
= Exp(6.1517)
= $469.54
Bottom border of price channel:
Exp(Y1,179)
= Exp(a + b × X1,179 – 2 × s)
= Exp(a + b × 1,710 – 2 × s)
= Exp(8.4076 + -0.0013 × 1,710 – 2 × 0.0224)
= Exp(6.0622)
= $429.32
March 27, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(8.4076 + -0.0013 × 1,823 + 2 × 0.0224)
= Exp(5.9997)
= $403.31
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(8.4076 + -0.0013 × 1,823 – 2 × 0.0224)
= Exp(5.9102)
= $368.77
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.80% per annum.
- MSFT price at the close of March 27, 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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