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 5.52% per annum.
- XOM price at the close of May 7, 2025 was $104.61 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.76% per annum.
- XOM price at the close of May 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 6, 2022
End date: May 7, 2025
a = 4.4639
b = 0.0001
s = 0.0531
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0531) – 1
= 23.69%
October 6, 2022 calculations
Top border of price channel:
Exp(Y608)
= Exp(a + b × X608 + 2 × s)
= Exp(a + b × 881 + 2 × s)
= Exp(4.4639 + 0.0001 × 881 + 2 × 0.0531)
= Exp(4.6999)
= $109.93
Bottom border of price channel:
Exp(Y608)
= Exp(a + b × X608 – 2 × s)
= Exp(a + b × 881 – 2 × s)
= Exp(4.4639 + 0.0001 × 881 – 2 × 0.0531)
= Exp(4.4873)
= $88.88
May 7, 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(4.4639 + 0.0001 × 1,825 + 2 × 0.0531)
= Exp(4.8388)
= $126.32
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.4639 + 0.0001 × 1,825 – 2 × 0.0531)
= Exp(4.6262)
= $102.13
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.52% per annum.
- XOM price at the close of May 7, 2025 was $104.61 and was inside the primary price channel.
Secondary Trend
Start date: March 28, 2024
End date: May 7, 2025
a = 4.9378
b = -0.0001
s = 0.0376
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0376) – 1
= 16.22%
March 28, 2024 calculations
Top border of price channel:
Exp(Y978)
= Exp(a + b × X978 + 2 × s)
= Exp(a + b × 1,420 + 2 × s)
= Exp(4.9378 + -0.0001 × 1,420 + 2 × 0.0376)
= Exp(4.8231)
= $124.35
Bottom border of price channel:
Exp(Y978)
= Exp(a + b × X978 – 2 × s)
= Exp(a + b × 1,420 – 2 × s)
= Exp(4.9378 + -0.0001 × 1,420 – 2 × 0.0376)
= Exp(4.6728)
= $107.00
May 7, 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(4.9378 + -0.0001 × 1,825 + 2 × 0.0376)
= Exp(4.7690)
= $117.80
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.9378 + -0.0001 × 1,825 – 2 × 0.0376)
= Exp(4.6187)
= $101.36
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.76% per annum.
- XOM price at the close of May 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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