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 13.36% per annum.
- CSX price at the close of April 20, 2023 was $30.81 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 169.42% per annum.
- CSX price at the close of April 20, 2023 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 CSX 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 15, 2021
End date: April 20, 2023
a = 4.0839
b = -0.0004
s = 0.0604
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -13.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0604) – 1
= 27.30%
October 15, 2021 calculations
Top border of price channel:
Exp(Y878)
= Exp(a + b × X878 + 2 × s)
= Exp(a + b × 1,271 + 2 × s)
= Exp(4.0839 + -0.0004 × 1,271 + 2 × 0.0604)
= Exp(3.7052)
= $40.66
Bottom border of price channel:
Exp(Y878)
= Exp(a + b × X878 – 2 × s)
= Exp(a + b × 1,271 – 2 × s)
= Exp(4.0839 + -0.0004 × 1,271 – 2 × 0.0604)
= Exp(3.4638)
= $31.94
April 20, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.0839 + -0.0004 × 1,823 + 2 × 0.0604)
= Exp(3.4884)
= $32.73
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.0839 + -0.0004 × 1,823 – 2 × 0.0604)
= Exp(3.2470)
= $25.71
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 13.36% per annum.
- CSX price at the close of April 20, 2023 was $30.81 and was inside the primary price channel.
Secondary Trend
Start date: March 22, 2023
End date: April 20, 2023
a = -1.5201
b = 0.0027
s = 0.0111
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0027) – 1
= 169.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0111) – 1
= 4.56%
March 22, 2023 calculations
Top border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 + 2 × s)
= Exp(a + b × 1,794 + 2 × s)
= Exp(-1.5201 + 0.0027 × 1,794 + 2 × 0.0111)
= Exp(3.3735)
= $29.18
Bottom border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 – 2 × s)
= Exp(a + b × 1,794 – 2 × s)
= Exp(-1.5201 + 0.0027 × 1,794 – 2 × 0.0111)
= Exp(3.3289)
= $27.91
April 20, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(-1.5201 + 0.0027 × 1,823 + 2 × 0.0111)
= Exp(3.4522)
= $31.57
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(-1.5201 + 0.0027 × 1,823 – 2 × 0.0111)
= Exp(3.4076)
= $30.19
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 169.42% per annum.
- CSX price at the close of April 20, 2023 was inside the secondary price channel.
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