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 5.75% per annum.
- XOM price at the close of April 28, 2025 was $108.63 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.26% per annum.
- XOM price at the close of April 28, 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 XOM 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: October 5, 2022
End date: April 28, 2025
a = 4.4551
b = 0.0002
s = 0.0529
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 5.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0529) – 1
= 23.56%
October 5, 2022 calculations
Top border of price channel:
Exp(Y614)
= Exp(a + b × X614 + 2 × s)
= Exp(a + b × 889 + 2 × s)
= Exp(4.4551 + 0.0002 × 889 + 2 × 0.0529)
= Exp(4.6971)
= $109.63
Bottom border of price channel:
Exp(Y614)
= Exp(a + b × X614 – 2 × s)
= Exp(a + b × 889 – 2 × s)
= Exp(4.4551 + 0.0002 × 889 – 2 × 0.0529)
= Exp(4.4855)
= $88.72
April 28, 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(4.4551 + 0.0002 × 1,825 + 2 × 0.0529)
= Exp(4.8405)
= $126.53
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.4551 + 0.0002 × 1,825 – 2 × 0.0529)
= Exp(4.6289)
= $102.40
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.75% per annum.
- XOM price at the close of April 28, 2025 was $108.63 and was inside the primary price channel.
Secondary Trend
Start date: March 28, 2024
End date: April 28, 2025
a = 4.9165
b = -0.0001
s = 0.0375
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.26%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0375) – 1
= 16.19%
March 28, 2024 calculations
Top border of price channel:
Exp(Y985)
= Exp(a + b × X985 + 2 × s)
= Exp(a + b × 1,429 + 2 × s)
= Exp(4.9165 + -0.0001 × 1,429 + 2 × 0.0375)
= Exp(4.8211)
= $124.10
Bottom border of price channel:
Exp(Y985)
= Exp(a + b × X985 – 2 × s)
= Exp(a + b × 1,429 – 2 × s)
= Exp(4.9165 + -0.0001 × 1,429 – 2 × 0.0375)
= Exp(4.6710)
= $106.81
April 28, 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(4.9165 + -0.0001 × 1,825 + 2 × 0.0375)
= Exp(4.7738)
= $118.37
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.9165 + -0.0001 × 1,825 – 2 × 0.0375)
= Exp(4.6238)
= $101.88
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.26% per annum.
- XOM price at the close of April 28, 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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