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 48.11% per annum.
- XOM price at the close of April 23, 2024 was $121.03 and was lower than the bottom border of the primary price channel by $21.21 (14.91%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 5.31% per annum.
- XOM price at the close of April 23, 2024 was higher than the top border of the secondary price channel by $8.96 (8.00%). This indicates a possible reversal in the secondary trend direction.
- 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: March 9, 2020
End date: May 10, 2023
a = 3.2137
b = 0.0011
s = 0.1105
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 48.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1105) – 1
= 55.60%
March 9, 2020 calculations
Top border of price channel:
Exp(Y220)
= Exp(a + b × X220 + 2 × s)
= Exp(a + b × 320 + 2 × s)
= Exp(3.2137 + 0.0011 × 320 + 2 × 0.1105)
= Exp(3.7791)
= $43.78
Bottom border of price channel:
Exp(Y220)
= Exp(a + b × X220 – 2 × s)
= Exp(a + b × 320 – 2 × s)
= Exp(3.2137 + 0.0011 × 320 – 2 × 0.1105)
= Exp(3.3370)
= $28.13
May 10, 2023 calculations
Top border of price channel:
Exp(Y1,019)
= Exp(a + b × X1,019 + 2 × s)
= Exp(a + b × 1,477 + 2 × s)
= Exp(3.2137 + 0.0011 × 1,477 + 2 × 0.1105)
= Exp(5.0241)
= $152.04
Bottom border of price channel:
Exp(Y1,019)
= Exp(a + b × X1,019 – 2 × s)
= Exp(a + b × 1,477 – 2 × s)
= Exp(3.2137 + 0.0011 × 1,477 – 2 × 0.1105)
= Exp(4.5820)
= $97.71
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 48.11% per annum.
- XOM price at the close of April 23, 2024 was $121.03 and was lower than the bottom border of the primary price channel by $21.21 (14.91%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 19, 2022
End date: March 13, 2024
a = 4.9081
b = -0.0001
s = 0.0419
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -5.31%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0419) – 1
= 18.26%
October 19, 2022 calculations
Top border of price channel:
Exp(Y880)
= Exp(a + b × X880 + 2 × s)
= Exp(a + b × 1,274 + 2 × s)
= Exp(4.9081 + -0.0001 × 1,274 + 2 × 0.0419)
= Exp(4.8016)
= $121.70
Bottom border of price channel:
Exp(Y880)
= Exp(a + b × X880 – 2 × s)
= Exp(a + b × 1,274 – 2 × s)
= Exp(4.9081 + -0.0001 × 1,274 – 2 × 0.0419)
= Exp(4.6338)
= $102.91
March 13, 2024 calculations
Top border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 + 2 × s)
= Exp(a + b × 1,785 + 2 × s)
= Exp(4.9081 + -0.0001 × 1,785 + 2 × 0.0419)
= Exp(4.7252)
= $112.76
Bottom border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 – 2 × s)
= Exp(a + b × 1,785 – 2 × s)
= Exp(4.9081 + -0.0001 × 1,785 – 2 × 0.0419)
= Exp(4.5575)
= $95.34
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 5.31% per annum.
- XOM price at the close of April 23, 2024 was higher than the top border of the secondary price channel by $8.96 (8.00%). This indicates a possible reversal in the secondary trend direction.
- 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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