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 30.79% per annum.
- CAT price at the close of October 14, 2026 was $748.98 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 50.52% per annum.
- CAT price at the close of October 14, 2026 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: April 30, 2026
End date: October 14, 2026
a = 7.1658
b = -0.0010
s = 0.0535
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -30.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0535) – 1
= 23.88%
April 30, 2026 calculations
Top border of price channel:
Exp(Y215)
= Exp(a + b × X215 + 2 × s)
= Exp(a + b × 311 + 2 × s)
= Exp(7.1658 + -0.0010 × 311 + 2 × 0.0535)
= Exp(6.9594)
= $1,052.96
Bottom border of price channel:
Exp(Y215)
= Exp(a + b × X215 – 2 × s)
= Exp(a + b × 311 – 2 × s)
= Exp(7.1658 + -0.0010 × 311 – 2 × 0.0535)
= Exp(6.7452)
= $849.96
October 14, 2026 calculations
Top border of price channel:
Exp(Y330)
= Exp(a + b × X330 + 2 × s)
= Exp(a + b × 478 + 2 × s)
= Exp(7.1658 + -0.0010 × 478 + 2 × 0.0535)
= Exp(6.7910)
= $889.81
Bottom border of price channel:
Exp(Y330)
= Exp(a + b × X330 – 2 × s)
= Exp(a + b × 478 – 2 × s)
= Exp(7.1658 + -0.0010 × 478 – 2 × 0.0535)
= Exp(6.5768)
= $718.26
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 30.79% per annum.
- CAT price at the close of October 14, 2026 was $748.98 and was inside the primary price channel.
Secondary Trend
Start date: June 16, 2026
End date: October 14, 2026
a = 7.5630
b = -0.0019
s = 0.0451
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0019) – 1
= -50.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0451) – 1
= 19.76%
June 16, 2026 calculations
Top border of price channel:
Exp(Y247)
= Exp(a + b × X247 + 2 × s)
= Exp(a + b × 358 + 2 × s)
= Exp(7.5630 + -0.0019 × 358 + 2 × 0.0451)
= Exp(6.9629)
= $1,056.74
Bottom border of price channel:
Exp(Y247)
= Exp(a + b × X247 – 2 × s)
= Exp(a + b × 358 – 2 × s)
= Exp(7.5630 + -0.0019 × 358 – 2 × 0.0451)
= Exp(6.7827)
= $882.41
October 14, 2026 calculations
Top border of price channel:
Exp(Y330)
= Exp(a + b × X330 + 2 × s)
= Exp(a + b × 478 + 2 × s)
= Exp(7.5630 + -0.0019 × 478 + 2 × 0.0451)
= Exp(6.7316)
= $838.49
Bottom border of price channel:
Exp(Y330)
= Exp(a + b × X330 – 2 × s)
= Exp(a + b × 478 – 2 × s)
= Exp(7.5630 + -0.0019 × 478 – 2 × 0.0451)
= Exp(6.5513)
= $700.16
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 50.52% per annum.
- CAT price at the close of October 14, 2026 was inside the secondary price channel.