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 0.93% per annum.
- PM price at the close of July 27, 2023 was $98.58 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 79.25% per annum.
- PM price at the close of July 27, 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 PM 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: April 29, 2021
End date: July 27, 2023
a = 4.6164
b = 0.0000
s = 0.0499
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0499) – 1
= 22.07%
April 29, 2021 calculations
Top border of price channel:
Exp(Y692)
= Exp(a + b × X692 + 2 × s)
= Exp(a + b × 1,004 + 2 × s)
= Exp(4.6164 + 0.0000 × 1,004 + 2 × 0.0499)
= Exp(4.6902)
= $108.88
Bottom border of price channel:
Exp(Y692)
= Exp(a + b × X692 – 2 × s)
= Exp(a + b × 1,004 – 2 × s)
= Exp(4.6164 + 0.0000 × 1,004 – 2 × 0.0499)
= Exp(4.4908)
= $89.20
July 27, 2023 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.6164 + 0.0000 × 1,823 + 2 × 0.0499)
= Exp(4.6692)
= $106.61
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.6164 + 0.0000 × 1,823 – 2 × 0.0499)
= Exp(4.4698)
= $87.34
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.93% per annum.
- PM price at the close of July 27, 2023 was $98.58 and was inside the primary price channel.
Secondary Trend
Start date: May 25, 2023
End date: July 27, 2023
a = 1.6931
b = 0.0016
s = 0.0132
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 79.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0132) – 1
= 5.44%
May 25, 2023 calculations
Top border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 + 2 × s)
= Exp(a + b × 1,760 + 2 × s)
= Exp(1.6931 + 0.0016 × 1,760 + 2 × 0.0132)
= Exp(4.5337)
= $93.10
Bottom border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 – 2 × s)
= Exp(a + b × 1,760 – 2 × s)
= Exp(1.6931 + 0.0016 × 1,760 – 2 × 0.0132)
= Exp(4.4807)
= $88.30
July 27, 2023 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(1.6931 + 0.0016 × 1,823 + 2 × 0.0132)
= Exp(4.6344)
= $102.97
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(1.6931 + 0.0016 × 1,823 – 2 × 0.0132)
= Exp(4.5814)
= $97.66
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 79.25% per annum.
- PM price at the close of July 27, 2023 was inside the secondary price channel.
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