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 10.75% per annum.
- MSFT price at the close of April 30, 2025 was $395.26 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 37.53% per annum.
- MSFT price at the close of April 30, 2025 was higher than the top border of the secondary price channel by $4.32 (1.10%). This indicates a possible reversal in the secondary trend direction.
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 15, 2024
End date: April 30, 2025
a = 6.5464
b = -0.0003
s = 0.0414
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0414) – 1
= 18.01%
May 15, 2024 calculations
Top border of price channel:
Exp(Y1,016)
= Exp(a + b × X1,016 + 2 × s)
= Exp(a + b × 1,475 + 2 × s)
= Exp(6.5464 + -0.0003 × 1,475 + 2 × 0.0414)
= Exp(6.1695)
= $477.95
Bottom border of price channel:
Exp(Y1,016)
= Exp(a + b × X1,016 – 2 × s)
= Exp(a + b × 1,475 – 2 × s)
= Exp(6.5464 + -0.0003 × 1,475 – 2 × 0.0414)
= Exp(6.0039)
= $404.99
April 30, 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(6.5464 + -0.0003 × 1,825 + 2 × 0.0414)
= Exp(6.0604)
= $428.55
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.5464 + -0.0003 × 1,825 – 2 × 0.0414)
= Exp(5.8948)
= $363.14
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.75% per annum.
- MSFT price at the close of April 30, 2025 was $395.26 and was inside the primary price channel.
Secondary Trend
Start date: December 4, 2024
End date: April 30, 2025
a = 8.2669
b = -0.0013
s = 0.0272
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -37.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0272) – 1
= 11.51%
December 4, 2024 calculations
Top border of price channel:
Exp(Y1,156)
= Exp(a + b × X1,156 + 2 × s)
= Exp(a + b × 1,678 + 2 × s)
= Exp(8.2669 + -0.0013 × 1,678 + 2 × 0.0272)
= Exp(6.1581)
= $472.52
Bottom border of price channel:
Exp(Y1,156)
= Exp(a + b × X1,156 – 2 × s)
= Exp(a + b × 1,678 – 2 × s)
= Exp(8.2669 + -0.0013 × 1,678 – 2 × 0.0272)
= Exp(6.0492)
= $423.76
April 30, 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(8.2669 + -0.0013 × 1,825 + 2 × 0.0272)
= Exp(5.9686)
= $390.94
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(8.2669 + -0.0013 × 1,825 – 2 × 0.0272)
= Exp(5.8597)
= $350.61
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 37.53% per annum.
- MSFT price at the close of April 30, 2025 was higher than the top border of the secondary price channel by $4.32 (1.10%). This indicates a possible reversal in the secondary trend direction.
- 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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