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 53.90% per annum.
- PYPL price at the close of May 9, 2023 was $65.90 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 13.22% per annum.
- PYPL price at the close of May 9, 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 PYPL 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: February 1, 2021
End date: May 9, 2023
a = 7.9051
b = -0.0021
s = 0.2133
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0021) – 1
= -53.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.2133) – 1
= 134.73%
February 1, 2021 calculations
Top border of price channel:
Exp(Y686)
= Exp(a + b × X686 + 2 × s)
= Exp(a + b × 998 + 2 × s)
= Exp(7.9051 + -0.0021 × 998 + 2 × 0.2133)
= Exp(6.2143)
= $499.85
Bottom border of price channel:
Exp(Y686)
= Exp(a + b × X686 – 2 × s)
= Exp(a + b × 998 – 2 × s)
= Exp(7.9051 + -0.0021 × 998 – 2 × 0.2133)
= Exp(5.3610)
= $212.95
May 9, 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(7.9051 + -0.0021 × 1,825 + 2 × 0.2133)
= Exp(4.4597)
= $86.46
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.9051 + -0.0021 × 1,825 – 2 × 0.2133)
= Exp(3.6064)
= $36.83
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 53.90% per annum.
- PYPL price at the close of May 9, 2023 was $65.90 and was inside the primary price channel.
Secondary Trend
Start date: April 20, 2022
End date: May 9, 2023
a = 5.0244
b = -0.0004
s = 0.0892
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -13.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0892) – 1
= 42.88%
April 20, 2022 calculations
Top border of price channel:
Exp(Y993)
= Exp(a + b × X993 + 2 × s)
= Exp(a + b × 1,441 + 2 × s)
= Exp(5.0244 + -0.0004 × 1,441 + 2 × 0.0892)
= Exp(4.6428)
= $103.83
Bottom border of price channel:
Exp(Y993)
= Exp(a + b × X993 – 2 × s)
= Exp(a + b × 1,441 – 2 × s)
= Exp(5.0244 + -0.0004 × 1,441 – 2 × 0.0892)
= Exp(4.2859)
= $72.67
May 9, 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(5.0244 + -0.0004 × 1,825 + 2 × 0.0892)
= Exp(4.4935)
= $89.44
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.0244 + -0.0004 × 1,825 – 2 × 0.0892)
= Exp(4.1367)
= $62.60
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 13.22% per annum.
- PYPL price at the close of May 9, 2023 was inside the secondary price channel.
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