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 177.28% per annum.
- CAT price at the close of April 18, 2024 was $357.93 and was lower than the bottom border of the primary price channel by $3.09 (0.86%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 70.79% per annum.
- CAT price at the close of April 18, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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: October 25, 2023
End date: April 15, 2024
a = 0.8515
b = 0.0028
s = 0.0282
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0028) – 1
= 177.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0282) – 1
= 11.92%
October 25, 2023 calculations
Top border of price channel:
Exp(Y1,137)
= Exp(a + b × X1,137 + 2 × s)
= Exp(a + b × 1,647 + 2 × s)
= Exp(0.8515 + 0.0028 × 1,647 + 2 × 0.0282)
= Exp(5.5098)
= $247.10
Bottom border of price channel:
Exp(Y1,137)
= Exp(a + b × X1,137 – 2 × s)
= Exp(a + b × 1,647 – 2 × s)
= Exp(0.8515 + 0.0028 × 1,647 – 2 × 0.0282)
= Exp(5.3972)
= $220.78
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(0.8515 + 0.0028 × 1,820 + 2 × 0.0282)
= Exp(5.9932)
= $400.68
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(0.8515 + 0.0028 × 1,820 – 2 × 0.0282)
= Exp(5.8806)
= $358.01
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 177.28% per annum.
- CAT price at the close of April 18, 2024 was $357.93 and was lower than the bottom border of the primary price channel by $3.09 (0.86%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 3, 2024
End date: April 18, 2024
a = 12.0309
b = -0.0034
s = 0.0089
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0034) – 1
= -70.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0089) – 1
= 3.64%
April 3, 2024 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,808 + 2 × s)
= Exp(12.0309 + -0.0034 × 1,808 + 2 × 0.0089)
= Exp(5.9525)
= $384.73
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,808 – 2 × s)
= Exp(12.0309 + -0.0034 × 1,808 – 2 × 0.0089)
= Exp(5.9168)
= $371.22
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(12.0309 + -0.0034 × 1,823 + 2 × 0.0089)
= Exp(5.9020)
= $365.76
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(12.0309 + -0.0034 × 1,823 – 2 × 0.0089)
= Exp(5.8662)
= $352.91
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 70.79% per annum.
- CAT price at the close of April 18, 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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