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 47.19% per annum.
- IBM price at the close of April 22, 2025 was $240.90 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.44% per annum.
- IBM price at the close of April 22, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 IBM 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: February 23, 2023
End date: April 3, 2025
a = 3.6159
b = 0.0011
s = 0.0573
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 47.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0573) – 1
= 25.75%
February 23, 2023 calculations
Top border of price channel:
Exp(Y714)
= Exp(a + b × X714 + 2 × s)
= Exp(a + b × 1,036 + 2 × s)
= Exp(3.6159 + 0.0011 × 1,036 + 2 × 0.0573)
= Exp(4.8276)
= $124.92
Bottom border of price channel:
Exp(Y714)
= Exp(a + b × X714 – 2 × s)
= Exp(a + b × 1,036 – 2 × s)
= Exp(3.6159 + 0.0011 × 1,036 – 2 × 0.0573)
= Exp(4.5985)
= $99.34
April 3, 2025 calculations
Top border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 + 2 × s)
= Exp(a + b × 1,806 + 2 × s)
= Exp(3.6159 + 0.0011 × 1,806 + 2 × 0.0573)
= Exp(5.6431)
= $282.35
Bottom border of price channel:
Exp(Y1,243)
= Exp(a + b × X1,243 – 2 × s)
= Exp(a + b × 1,806 – 2 × s)
= Exp(3.6159 + 0.0011 × 1,806 – 2 × 0.0573)
= Exp(5.4141)
= $224.54
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 47.19% per annum.
- IBM price at the close of April 22, 2025 was $240.90 and was inside the primary price channel.
Secondary Trend
Start date: January 30, 2025
End date: April 22, 2025
a = 7.8883
b = -0.0013
s = 0.0259
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -38.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0259) – 1
= 10.90%
January 30, 2025 calculations
Top border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 + 2 × s)
= Exp(a + b × 1,743 + 2 × s)
= Exp(7.8883 + -0.0013 × 1,743 + 2 × 0.0259)
= Exp(5.6234)
= $276.83
Bottom border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 – 2 × s)
= Exp(a + b × 1,743 – 2 × s)
= Exp(7.8883 + -0.0013 × 1,743 – 2 × 0.0259)
= Exp(5.5200)
= $249.63
April 22, 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(7.8883 + -0.0013 × 1,825 + 2 × 0.0259)
= Exp(5.5144)
= $248.25
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.8883 + -0.0013 × 1,825 – 2 × 0.0259)
= Exp(5.4110)
= $223.85
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.44% per annum.
- IBM price at the close of April 22, 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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