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 79.71% per annum.
- PSX price at the close of February 21, 2020 was $89.25 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.44% per annum.
- PSX price at the close of February 21, 2020 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 PSX 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: December 16, 2019
End date: February 21, 2020
a = 12.4387
b = -0.0044
s = 0.0224
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0044) – 1
= -79.71%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0224) – 1
= 9.39%
December 16, 2019 calculations
Top border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 + 2 × s)
= Exp(a + b × 1,757 + 2 × s)
= Exp(12.4387 + -0.0044 × 1,757 + 2 × 0.0224)
= Exp(4.8050)
= $122.12
Bottom border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 – 2 × s)
= Exp(a + b × 1,757 – 2 × s)
= Exp(12.4387 + -0.0044 × 1,757 – 2 × 0.0224)
= Exp(4.7152)
= $111.64
February 21, 2020 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(12.4387 + -0.0044 × 1,824 + 2 × 0.0224)
= Exp(4.5122)
= $91.12
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(12.4387 + -0.0044 × 1,824 – 2 × 0.0224)
= Exp(4.4224)
= $83.30
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 79.71% per annum.
- PSX price at the close of February 21, 2020 was $89.25 and was inside the primary price channel.
Secondary Trend
Start date: January 31, 2020
End date: February 21, 2020
a = 6.0934
b = -0.0009
s = 0.0127
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -27.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0127) – 1
= 5.19%
January 31, 2020 calculations
Top border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 + 2 × s)
= Exp(a + b × 1,803 + 2 × s)
= Exp(6.0934 + -0.0009 × 1,803 + 2 × 0.0127)
= Exp(4.5342)
= $93.15
Bottom border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 – 2 × s)
= Exp(a + b × 1,803 – 2 × s)
= Exp(6.0934 + -0.0009 × 1,803 – 2 × 0.0127)
= Exp(4.4836)
= $88.55
February 21, 2020 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.0934 + -0.0009 × 1,824 + 2 × 0.0127)
= Exp(4.5158)
= $91.45
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.0934 + -0.0009 × 1,824 – 2 × 0.0127)
= Exp(4.4652)
= $86.93
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.44% per annum.
- PSX price at the close of February 21, 2020 was inside the secondary price channel.
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