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 9.05% per annum.
- MO price at the close of April 26, 2024 was $43.38 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.60% per annum.
- MO price at the close of April 26, 2024 was inside the secondary price channel.
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 MO 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: January 3, 2022
End date: April 22, 2024
a = 4.1764
b = -0.0003
s = 0.0550
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -9.05%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0550) – 1
= 24.63%
January 3, 2022 calculations
Top border of price channel:
Exp(Y677)
= Exp(a + b × X677 + 2 × s)
= Exp(a + b × 980 + 2 × s)
= Exp(4.1764 + -0.0003 × 980 + 2 × 0.0550)
= Exp(4.0316)
= $56.35
Bottom border of price channel:
Exp(Y677)
= Exp(a + b × X677 – 2 × s)
= Exp(a + b × 980 – 2 × s)
= Exp(4.1764 + -0.0003 × 980 – 2 × 0.0550)
= Exp(3.8114)
= $45.21
April 22, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(4.1764 + -0.0003 × 1,820 + 2 × 0.0550)
= Exp(3.8132)
= $45.29
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(4.1764 + -0.0003 × 1,820 – 2 × 0.0550)
= Exp(3.5930)
= $36.34
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 9.05% per annum.
- MO price at the close of April 26, 2024 was $43.38 and was inside the primary price channel.
Secondary Trend
Start date: June 14, 2022
End date: April 26, 2024
a = 3.9701
b = -0.0001
s = 0.0413
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.60%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0413) – 1
= 17.97%
June 14, 2022 calculations
Top border of price channel:
Exp(Y789)
= Exp(a + b × X789 + 2 × s)
= Exp(a + b × 1,142 + 2 × s)
= Exp(3.9701 + -0.0001 × 1,142 + 2 × 0.0413)
= Exp(3.9053)
= $49.66
Bottom border of price channel:
Exp(Y789)
= Exp(a + b × X789 – 2 × s)
= Exp(a + b × 1,142 – 2 × s)
= Exp(3.9701 + -0.0001 × 1,142 – 2 × 0.0413)
= Exp(3.7400)
= $42.10
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.9701 + -0.0001 × 1,824 + 2 × 0.0413)
= Exp(3.8172)
= $45.48
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.9701 + -0.0001 × 1,824 – 2 × 0.0413)
= Exp(3.6520)
= $38.55
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.60% per annum.
- MO price at the close of April 26, 2024 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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