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 39.64% per annum.
- CAT price at the close of February 20, 2025 was $349.15 and was lower than the bottom border of the primary price channel by $10.04 (2.79%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 18.56% per annum.
- CAT price at the close of February 20, 2025 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: June 16, 2022
End date: December 17, 2024
a = 4.3767
b = 0.0009
s = 0.0817
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.64%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0817) – 1
= 38.67%
June 16, 2022 calculations
Top border of price channel:
Exp(Y585)
= Exp(a + b × X585 + 2 × s)
= Exp(a + b × 846 + 2 × s)
= Exp(4.3767 + 0.0009 × 846 + 2 × 0.0817)
= Exp(5.3142)
= $203.20
Bottom border of price channel:
Exp(Y585)
= Exp(a + b × X585 – 2 × s)
= Exp(a + b × 846 – 2 × s)
= Exp(4.3767 + 0.0009 × 846 – 2 × 0.0817)
= Exp(4.9873)
= $146.53
December 17, 2024 calculations
Top border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 + 2 × s)
= Exp(a + b × 1,761 + 2 × s)
= Exp(4.3767 + 0.0009 × 1,761 + 2 × 0.0817)
= Exp(6.1513)
= $469.32
Bottom border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 – 2 × s)
= Exp(a + b × 1,761 – 2 × s)
= Exp(4.3767 + 0.0009 × 1,761 – 2 × 0.0817)
= Exp(5.8244)
= $338.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 39.64% per annum.
- CAT price at the close of February 20, 2025 was $349.15 and was lower than the bottom border of the primary price channel by $10.04 (2.79%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: September 26, 2024
End date: February 20, 2025
a = 6.9265
b = -0.0006
s = 0.0343
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -18.56%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0343) – 1
= 14.72%
September 26, 2024 calculations
Top border of price channel:
Exp(Y1,157)
= Exp(a + b × X1,157 + 2 × s)
= Exp(a + b × 1,679 + 2 × s)
= Exp(6.9265 + -0.0006 × 1,679 + 2 × 0.0343)
= Exp(6.0509)
= $424.49
Bottom border of price channel:
Exp(Y1,157)
= Exp(a + b × X1,157 – 2 × s)
= Exp(a + b × 1,679 – 2 × s)
= Exp(6.9265 + -0.0006 × 1,679 – 2 × 0.0343)
= Exp(5.9136)
= $370.03
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.9265 + -0.0006 × 1,826 + 2 × 0.0343)
= Exp(5.9682)
= $390.81
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.9265 + -0.0006 × 1,826 – 2 × 0.0343)
= Exp(5.8309)
= $340.67
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 18.56% per annum.
- CAT price at the close of February 20, 2025 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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