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 37.38% per annum.
- PFE price at the close of April 25, 2024 was $25.26 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 22.98% per annum.
- PFE price at the close of April 25, 2024 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 PFE 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: November 1, 2022
End date: April 25, 2024
a = 5.5664
b = -0.0013
s = 0.0411
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -37.38%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0411) – 1
= 17.85%
November 1, 2022 calculations
Top border of price channel:
Exp(Y887)
= Exp(a + b × X887 + 2 × s)
= Exp(a + b × 1,285 + 2 × s)
= Exp(5.5664 + -0.0013 × 1,285 + 2 × 0.0411)
= Exp(4.0009)
= $54.65
Bottom border of price channel:
Exp(Y887)
= Exp(a + b × X887 – 2 × s)
= Exp(a + b × 1,285 – 2 × s)
= Exp(5.5664 + -0.0013 × 1,285 – 2 × 0.0411)
= Exp(3.8367)
= $46.37
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.5664 + -0.0013 × 1,826 + 2 × 0.0411)
= Exp(3.3072)
= $27.31
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.5664 + -0.0013 × 1,826 – 2 × 0.0411)
= Exp(3.1430)
= $23.17
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.38% per annum.
- PFE price at the close of April 25, 2024 was $25.26 and was inside the primary price channel.
Secondary Trend
Start date: November 9, 2023
End date: April 25, 2024
a = 4.5738
b = -0.0007
s = 0.0279
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -22.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0279) – 1
= 11.80%
November 9, 2023 calculations
Top border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 + 2 × s)
= Exp(a + b × 1,658 + 2 × s)
= Exp(4.5738 + -0.0007 × 1,658 + 2 × 0.0279)
= Exp(3.4435)
= $31.30
Bottom border of price channel:
Exp(Y1,144)
= Exp(a + b × X1,144 – 2 × s)
= Exp(a + b × 1,658 – 2 × s)
= Exp(4.5738 + -0.0007 × 1,658 – 2 × 0.0279)
= Exp(3.3319)
= $27.99
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.5738 + -0.0007 × 1,826 + 2 × 0.0279)
= Exp(3.3233)
= $27.75
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.5738 + -0.0007 × 1,826 – 2 × 0.0279)
= Exp(3.2117)
= $24.82
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 22.98% per annum.
- PFE price at the close of April 25, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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