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 6.14% per annum.
- XOM price at the close of April 8, 2025 was $100.77 and was lower than the bottom border of the primary price channel by $2.10 (2.04%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 3.08% per annum.
- XOM price at the close of April 8, 2025 was lower than the bottom border of the secondary price channel by $2.38 (2.31%).
- 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 8, 2025
a = 4.4398
b = 0.0002
s = 0.0522
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0522) – 1
= 23.20%
October 5, 2022 calculations
Top border of price channel:
Exp(Y627)
= Exp(a + b × X627 + 2 × s)
= Exp(a + b × 909 + 2 × s)
= Exp(4.4398 + 0.0002 × 909 + 2 × 0.0522)
= Exp(4.6925)
= $109.13
Bottom border of price channel:
Exp(Y627)
= Exp(a + b × X627 – 2 × s)
= Exp(a + b × 909 – 2 × s)
= Exp(4.4398 + 0.0002 × 909 – 2 × 0.0522)
= Exp(4.4839)
= $88.58
April 8, 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(4.4398 + 0.0002 × 1,825 + 2 × 0.0522)
= Exp(4.8421)
= $126.74
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.4398 + 0.0002 × 1,825 – 2 × 0.0522)
= Exp(4.6335)
= $102.87
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 6.14% per annum.
- XOM price at the close of April 8, 2025 was $100.77 and was lower than the bottom border of the primary price channel by $2.10 (2.04%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 28, 2024
End date: April 8, 2025
a = 4.8660
b = -0.0001
s = 0.0367
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -3.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0367) – 1
= 15.80%
March 28, 2024 calculations
Top border of price channel:
Exp(Y998)
= Exp(a + b × X998 + 2 × s)
= Exp(a + b × 1,449 + 2 × s)
= Exp(4.8660 + -0.0001 × 1,449 + 2 × 0.0367)
= Exp(4.8151)
= $123.36
Bottom border of price channel:
Exp(Y998)
= Exp(a + b × X998 – 2 × s)
= Exp(a + b × 1,449 – 2 × s)
= Exp(4.8660 + -0.0001 × 1,449 – 2 × 0.0367)
= Exp(4.6685)
= $106.53
April 8, 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(4.8660 + -0.0001 × 1,825 + 2 × 0.0367)
= Exp(4.7829)
= $119.45
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.8660 + -0.0001 × 1,825 – 2 × 0.0367)
= Exp(4.6362)
= $103.15
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 3.08% per annum.
- XOM price at the close of April 8, 2025 was lower than the bottom border of the secondary price channel by $2.38 (2.31%).
- 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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