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 6.22% per annum.
- XOM price at the close of March 7, 2025 was $109.02 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 25.37% per annum.
- XOM price at the close of March 7, 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: March 7, 2025
a = 4.4321
b = 0.0002
s = 0.0523
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0523) – 1
= 23.27%
October 5, 2022 calculations
Top border of price channel:
Exp(Y650)
= Exp(a + b × X650 + 2 × s)
= Exp(a + b × 940 + 2 × s)
= Exp(4.4321 + 0.0002 × 940 + 2 × 0.0523)
= Exp(4.6922)
= $109.09
Bottom border of price channel:
Exp(Y650)
= Exp(a + b × X650 – 2 × s)
= Exp(a + b × 940 – 2 × s)
= Exp(4.4321 + 0.0002 × 940 – 2 × 0.0523)
= Exp(4.4829)
= $88.50
March 7, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.4321 + 0.0002 × 1,824 + 2 × 0.0523)
= Exp(4.8384)
= $126.27
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.4321 + 0.0002 × 1,824 – 2 × 0.0523)
= Exp(4.6292)
= $102.43
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 6.22% per annum.
- XOM price at the close of March 7, 2025 was $109.02 and was inside the primary price channel.
Secondary Trend
Start date: October 1, 2024
End date: March 7, 2025
a = 6.1216
b = -0.0008
s = 0.0293
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -25.37%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0293) – 1
= 12.44%
October 1, 2024 calculations
Top border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 + 2 × s)
= Exp(a + b × 1,667 + 2 × s)
= Exp(6.1216 + -0.0008 × 1,667 + 2 × 0.0293)
= Exp(4.8440)
= $126.97
Bottom border of price channel:
Exp(Y1,149)
= Exp(a + b × X1,149 – 2 × s)
= Exp(a + b × 1,667 – 2 × s)
= Exp(6.1216 + -0.0008 × 1,667 – 2 × 0.0293)
= Exp(4.7267)
= $112.92
March 7, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.1216 + -0.0008 × 1,824 + 2 × 0.0293)
= Exp(4.7181)
= $111.96
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.1216 + -0.0008 × 1,824 – 2 × 0.0293)
= Exp(4.6009)
= $99.57
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 25.37% per annum.
- XOM price at the close of March 7, 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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