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 24.13% per annum.
- EL price at the close of August 18, 2023 was $156.69 and was lower than the bottom border of the primary price channel by $2.82 (1.77%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 57.21% per annum.
- EL price at the close of August 18, 2023 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 EL 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: June 24, 2021
End date: August 18, 2023
a = 6.6461
b = -0.0008
s = 0.0969
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -24.13%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0969) – 1
= 47.36%
June 24, 2021 calculations
Top border of price channel:
Exp(Y716)
= Exp(a + b × X716 + 2 × s)
= Exp(a + b × 1,039 + 2 × s)
= Exp(6.6461 + -0.0008 × 1,039 + 2 × 0.0969)
= Exp(6.0538)
= $425.73
Bottom border of price channel:
Exp(Y716)
= Exp(a + b × X716 – 2 × s)
= Exp(a + b × 1,039 – 2 × s)
= Exp(6.6461 + -0.0008 × 1,039 – 2 × 0.0969)
= Exp(5.6661)
= $288.91
August 18, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.6461 + -0.0008 × 1,824 + 2 × 0.0969)
= Exp(5.4599)
= $235.06
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.6461 + -0.0008 × 1,824 – 2 × 0.0969)
= Exp(5.0721)
= $159.51
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 24.13% per annum.
- EL price at the close of August 18, 2023 was $156.69 and was lower than the bottom border of the primary price channel by $2.82 (1.77%).
Secondary Trend
Start date: January 10, 2023
End date: August 18, 2023
a = 9.3695
b = -0.0023
s = 0.0574
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0023) – 1
= -57.21%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0574) – 1
= 25.82%
January 10, 2023 calculations
Top border of price channel:
Exp(Y1,105)
= Exp(a + b × X1,105 + 2 × s)
= Exp(a + b × 1,604 + 2 × s)
= Exp(9.3695 + -0.0023 × 1,604 + 2 × 0.0574)
= Exp(5.7538)
= $315.40
Bottom border of price channel:
Exp(Y1,105)
= Exp(a + b × X1,105 – 2 × s)
= Exp(a + b × 1,604 – 2 × s)
= Exp(9.3695 + -0.0023 × 1,604 – 2 × 0.0574)
= Exp(5.5241)
= $250.67
August 18, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(9.3695 + -0.0023 × 1,824 + 2 × 0.0574)
= Exp(5.2422)
= $189.08
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(9.3695 + -0.0023 × 1,824 – 2 × 0.0574)
= Exp(5.0125)
= $150.27
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 57.21% per annum.
- EL price at the close of August 18, 2023 was inside the secondary price channel.
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