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 19.23% per annum.
- HPQ price at the close of August 29, 2019 was $18.09 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 83.96% per annum.
- HPQ price at the close of August 29, 2019 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 HPQ 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 5, 2018
End date: August 29, 2019
a = 4.0173
b = -0.0006
s = 0.0603
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -19.23%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0603) – 1
= 27.27%
June 5, 2018 calculations
Top border of price channel:
Exp(Y946)
= Exp(a + b × X946 + 2 × s)
= Exp(a + b × 1,372 + 2 × s)
= Exp(4.0173 + -0.0006 × 1,372 + 2 × 0.0603)
= Exp(3.3351)
= $28.08
Bottom border of price channel:
Exp(Y946)
= Exp(a + b × X946 – 2 × s)
= Exp(a + b × 1,372 – 2 × s)
= Exp(4.0173 + -0.0006 × 1,372 – 2 × 0.0603)
= Exp(3.0940)
= $22.06
August 29, 2019 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(4.0173 + -0.0006 × 1,822 + 2 × 0.0603)
= Exp(3.0718)
= $21.58
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(4.0173 + -0.0006 × 1,822 – 2 × 0.0603)
= Exp(2.8307)
= $16.96
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 19.23% per annum.
- HPQ price at the close of August 29, 2019 was $18.09 and was inside the primary price channel.
Secondary Trend
Start date: July 18, 2019
End date: August 29, 2019
a = 12.0141
b = -0.0050
s = 0.0240
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0050) – 1
= -83.96%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0240) – 1
= 10.06%
July 18, 2019 calculations
Top border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 + 2 × s)
= Exp(a + b × 1,780 + 2 × s)
= Exp(12.0141 + -0.0050 × 1,780 + 2 × 0.0240)
= Exp(3.1364)
= $23.02
Bottom border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 – 2 × s)
= Exp(a + b × 1,780 – 2 × s)
= Exp(12.0141 + -0.0050 × 1,780 – 2 × 0.0240)
= Exp(3.0406)
= $20.92
August 29, 2019 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(12.0141 + -0.0050 × 1,822 + 2 × 0.0240)
= Exp(2.9258)
= $18.65
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(12.0141 + -0.0050 × 1,822 – 2 × 0.0240)
= Exp(2.8300)
= $16.95
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 83.96% per annum.
- HPQ price at the close of August 29, 2019 was inside the secondary price channel.
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