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 47.51% per annum.
- MSFT price at the close of February 20, 2025 was $416.13 and was lower than the bottom border of the primary price channel by $105.62 (20.24%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.17% per annum.
- MSFT price at the close of February 20, 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: September 1, 2022
End date: July 23, 2024
a = 4.4191
b = 0.0011
s = 0.0533
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 47.51%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0533) – 1
= 23.76%
September 1, 2022 calculations
Top border of price channel:
Exp(Y638)
= Exp(a + b × X638 + 2 × s)
= Exp(a + b × 923 + 2 × s)
= Exp(4.4191 + 0.0011 × 923 + 2 × 0.0533)
= Exp(5.5086)
= $246.82
Bottom border of price channel:
Exp(Y638)
= Exp(a + b × X638 – 2 × s)
= Exp(a + b × 923 – 2 × s)
= Exp(4.4191 + 0.0011 × 923 – 2 × 0.0533)
= Exp(5.2955)
= $199.44
July 23, 2024 calculations
Top border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 + 2 × s)
= Exp(a + b × 1,614 + 2 × s)
= Exp(4.4191 + 0.0011 × 1,614 + 2 × 0.0533)
= Exp(6.2446)
= $515.20
Bottom border of price channel:
Exp(Y1,111)
= Exp(a + b × X1,111 – 2 × s)
= Exp(a + b × 1,614 – 2 × s)
= Exp(4.4191 + 0.0011 × 1,614 – 2 × 0.0533)
= Exp(6.0314)
= $416.30
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 47.51% per annum.
- MSFT price at the close of February 20, 2025 was $416.13 and was lower than the bottom border of the primary price channel by $105.62 (20.24%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 18, 2024
End date: February 20, 2025
a = 5.8576
b = 0.0001
s = 0.0341
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.17%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0341) – 1
= 14.62%
January 18, 2024 calculations
Top border of price channel:
Exp(Y983)
= Exp(a + b × X983 + 2 × s)
= Exp(a + b × 1,427 + 2 × s)
= Exp(5.8576 + 0.0001 × 1,427 + 2 × 0.0341)
= Exp(6.0857)
= $439.53
Bottom border of price channel:
Exp(Y983)
= Exp(a + b × X983 – 2 × s)
= Exp(a + b × 1,427 – 2 × s)
= Exp(5.8576 + 0.0001 × 1,427 – 2 × 0.0341)
= Exp(5.9492)
= $383.46
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.8576 + 0.0001 × 1,826 + 2 × 0.0341)
= Exp(6.1304)
= $459.61
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.8576 + 0.0001 × 1,826 – 2 × 0.0341)
= Exp(5.9939)
= $400.99
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.17% per annum.
- MSFT price at the close of February 20, 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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