Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.75% per annum.
- OXY price at the close of February 20, 2025 was $52.09 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 32.91% per annum.
- OXY price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $2.16 (4.32%). This indicates a possible reversal in the secondary trend direction.
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 OXY 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: May 4, 2022
End date: February 20, 2025
a = 4.3310
b = -0.0002
s = 0.0738
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0738) – 1
= 34.31%
May 4, 2022 calculations
Top border of price channel:
Exp(Y555)
= Exp(a + b × X555 + 2 × s)
= Exp(a + b × 803 + 2 × s)
= Exp(4.3310 + -0.0002 × 803 + 2 × 0.0738)
= Exp(4.3248)
= $75.55
Bottom border of price channel:
Exp(Y555)
= Exp(a + b × X555 – 2 × s)
= Exp(a + b × 803 – 2 × s)
= Exp(4.3310 + -0.0002 × 803 – 2 × 0.0738)
= Exp(4.0298)
= $56.25
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.3310 + -0.0002 × 1,826 + 2 × 0.0738)
= Exp(4.1290)
= $62.11
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.3310 + -0.0002 × 1,826 – 2 × 0.0738)
= Exp(3.8339)
= $46.24
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.75% per annum.
- OXY price at the close of February 20, 2025 was $52.09 and was inside the primary price channel.
Secondary Trend
Start date: March 25, 2024
End date: February 20, 2025
a = 5.8293
b = -0.0011
s = 0.0389
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -32.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0389) – 1
= 16.85%
March 25, 2024 calculations
Top border of price channel:
Exp(Y1,029)
= Exp(a + b × X1,029 + 2 × s)
= Exp(a + b × 1,494 + 2 × s)
= Exp(5.8293 + -0.0011 × 1,494 + 2 × 0.0389)
= Exp(4.2737)
= $71.78
Bottom border of price channel:
Exp(Y1,029)
= Exp(a + b × X1,029 – 2 × s)
= Exp(a + b × 1,494 – 2 × s)
= Exp(5.8293 + -0.0011 × 1,494 – 2 × 0.0389)
= Exp(4.1179)
= $61.43
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.8293 + -0.0011 × 1,826 + 2 × 0.0389)
= Exp(3.9107)
= $49.93
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.8293 + -0.0011 × 1,826 – 2 × 0.0389)
= Exp(3.7549)
= $42.73
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 32.91% per annum.
- OXY price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $2.16 (4.32%). 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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