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 46.32% per annum.
- DG price at the close of August 31, 2023 was $138.50 and was lower than the bottom border of the primary price channel by $2.29 (1.62%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 8.93% per annum.
- DG price at the close of August 31, 2023 was lower than the bottom border of the secondary price channel by $11.84 (7.88%).
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 DG 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 25, 2022
End date: August 31, 2023
a = 8.1769
b = -0.0017
s = 0.0622
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0017) – 1
= -46.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0622) – 1
= 28.24%
October 25, 2022 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,512 + 2 × s)
= Exp(8.1769 + -0.0017 × 1,512 + 2 × 0.0622)
= Exp(5.7243)
= $306.23
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,512 – 2 × s)
= Exp(8.1769 + -0.0017 × 1,512 – 2 × 0.0622)
= Exp(5.4756)
= $238.79
August 31, 2023 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(8.1769 + -0.0017 × 1,822 + 2 × 0.0622)
= Exp(5.1960)
= $180.55
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(8.1769 + -0.0017 × 1,822 – 2 × 0.0622)
= Exp(4.9472)
= $140.79
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 46.32% per annum.
- DG price at the close of August 31, 2023 was $138.50 and was lower than the bottom border of the primary price channel by $2.29 (1.62%).
Secondary Trend
Start date: June 1, 2023
End date: August 31, 2023
a = 5.5543
b = -0.0003
s = 0.0372
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -8.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0372) – 1
= 16.02%
June 1, 2023 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,731 + 2 × s)
= Exp(5.5543 + -0.0003 × 1,731 + 2 × 0.0372)
= Exp(5.1849)
= $178.55
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,731 – 2 × s)
= Exp(5.5543 + -0.0003 × 1,731 – 2 × 0.0372)
= Exp(5.0362)
= $153.89
August 31, 2023 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(5.5543 + -0.0003 × 1,822 + 2 × 0.0372)
= Exp(5.1615)
= $174.43
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(5.5543 + -0.0003 × 1,822 – 2 × 0.0372)
= Exp(5.0129)
= $150.34
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 8.93% per annum.
- DG price at the close of August 31, 2023 was lower than the bottom border of the secondary price channel by $11.84 (7.88%).
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