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 39.70% per annum.
- CAT price at the close of November 19, 2024 was $382.33 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 20.15% per annum.
- CAT price at the close of November 19, 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 CAT 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 16, 2022
End date: November 19, 2024
a = 4.2939
b = 0.0009
s = 0.0828
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.70%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0828) – 1
= 39.27%
June 16, 2022 calculations
Top border of price channel:
Exp(Y647)
= Exp(a + b × X647 + 2 × s)
= Exp(a + b × 939 + 2 × s)
= Exp(4.2939 + 0.0009 × 939 + 2 × 0.0828)
= Exp(5.3196)
= $204.29
Bottom border of price channel:
Exp(Y647)
= Exp(a + b × X647 – 2 × s)
= Exp(a + b × 939 – 2 × s)
= Exp(4.2939 + 0.0009 × 939 – 2 × 0.0828)
= Exp(4.9883)
= $146.69
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.2939 + 0.0009 × 1,826 + 2 × 0.0828)
= Exp(6.1320)
= $460.35
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.2939 + 0.0009 × 1,826 – 2 × 0.0828)
= Exp(5.8007)
= $330.54
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 39.70% per annum.
- CAT price at the close of November 19, 2024 was $382.33 and was inside the primary price channel.
Secondary Trend
Start date: February 5, 2024
End date: November 19, 2024
a = 5.0089
b = 0.0005
s = 0.0545
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 20.15%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0545) – 1
= 24.34%
February 5, 2024 calculations
Top border of price channel:
Exp(Y1,057)
= Exp(a + b × X1,057 + 2 × s)
= Exp(a + b × 1,538 + 2 × s)
= Exp(5.0089 + 0.0005 × 1,538 + 2 × 0.0545)
= Exp(5.8914)
= $361.90
Bottom border of price channel:
Exp(Y1,057)
= Exp(a + b × X1,057 – 2 × s)
= Exp(a + b × 1,538 – 2 × s)
= Exp(5.0089 + 0.0005 × 1,538 – 2 × 0.0545)
= Exp(5.6735)
= $291.06
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.0089 + 0.0005 × 1,826 + 2 × 0.0545)
= Exp(6.0362)
= $418.31
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.0089 + 0.0005 × 1,826 – 2 × 0.0545)
= Exp(5.8184)
= $336.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 20.15% per annum.
- CAT price at the close of November 19, 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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