Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 5.15% per annum.
- AZO price at the close of December 18, 2023 was $2,637.36 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.11% per annum.
- AZO price at the close of December 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 AZO 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 24, 2022
End date: December 18, 2023
a = 7.6060
b = 0.0001
s = 0.0359
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.15%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0359) – 1
= 15.46%
October 24, 2022 calculations
Top border of price channel:
Exp(Y968)
= Exp(a + b × X968 + 2 × s)
= Exp(a + b × 1,405 + 2 × s)
= Exp(7.6060 + 0.0001 × 1,405 + 2 × 0.0359)
= Exp(7.8711)
= $2,620.38
Bottom border of price channel:
Exp(Y968)
= Exp(a + b × X968 – 2 × s)
= Exp(a + b × 1,405 – 2 × s)
= Exp(7.6060 + 0.0001 × 1,405 – 2 × 0.0359)
= Exp(7.7273)
= $2,269.50
December 18, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.6060 + 0.0001 × 1,825 + 2 × 0.0359)
= Exp(7.9288)
= $2,776.18
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.6060 + 0.0001 × 1,825 – 2 × 0.0359)
= Exp(7.7851)
= $2,404.44
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.15% per annum.
- AZO price at the close of December 18, 2023 was $2,637.36 and was inside the primary price channel.
Secondary Trend
Start date: May 24, 2023
End date: December 18, 2023
a = 7.0486
b = 0.0005
s = 0.0220
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 18.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0220) – 1
= 9.21%
May 24, 2023 calculations
Top border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 + 2 × s)
= Exp(a + b × 1,617 + 2 × s)
= Exp(7.0486 + 0.0005 × 1,617 + 2 × 0.0220)
= Exp(7.8298)
= $2,514.47
Bottom border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 – 2 × s)
= Exp(a + b × 1,617 – 2 × s)
= Exp(7.0486 + 0.0005 × 1,617 – 2 × 0.0220)
= Exp(7.7417)
= $2,302.34
December 18, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.0486 + 0.0005 × 1,825 + 2 × 0.0220)
= Exp(7.9246)
= $2,764.58
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.0486 + 0.0005 × 1,825 – 2 × 0.0220)
= Exp(7.8365)
= $2,531.35
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.11% per annum.
- AZO price at the close of December 18, 2023 was inside the secondary price channel.
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