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 80.41% per annum.
- CAT price at the close of August 14, 2026 was $856.57 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 291.98% per annum.
- CAT price at the close of August 14, 2026 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 18, 2026
End date: August 11, 2026
a = 8.5485
b = -0.0045
s = 0.0351
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0045) – 1
= -80.41%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0351) – 1
= 15.07%
June 18, 2026 calculations
Top border of price channel:
Exp(Y249)
= Exp(a + b × X249 + 2 × s)
= Exp(a + b × 360 + 2 × s)
= Exp(8.5485 + -0.0045 × 360 + 2 × 0.0351)
= Exp(7.0111)
= $1,108.88
Bottom border of price channel:
Exp(Y249)
= Exp(a + b × X249 – 2 × s)
= Exp(a + b × 360 – 2 × s)
= Exp(8.5485 + -0.0045 × 360 – 2 × 0.0351)
= Exp(6.8707)
= $963.64
August 11, 2026 calculations
Top border of price channel:
Exp(Y285)
= Exp(a + b × X285 + 2 × s)
= Exp(a + b × 414 + 2 × s)
= Exp(8.5485 + -0.0045 × 414 + 2 × 0.0351)
= Exp(6.7700)
= $871.28
Bottom border of price channel:
Exp(Y285)
= Exp(a + b × X285 – 2 × s)
= Exp(a + b × 414 – 2 × s)
= Exp(8.5485 + -0.0045 × 414 – 2 × 0.0351)
= Exp(6.6296)
= $757.16
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 80.41% per annum.
- CAT price at the close of August 14, 2026 was $856.57 and was inside the primary price channel.
Secondary Trend
Start date: July 29, 2026
End date: August 14, 2026
a = 5.2021
b = 0.0037
s = 0.0254
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0037) – 1
= 291.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0254) – 1
= 10.69%
July 29, 2026 calculations
Top border of price channel:
Exp(Y276)
= Exp(a + b × X276 + 2 × s)
= Exp(a + b × 401 + 2 × s)
= Exp(5.2021 + 0.0037 × 401 + 2 × 0.0254)
= Exp(6.7537)
= $857.20
Bottom border of price channel:
Exp(Y276)
= Exp(a + b × X276 – 2 × s)
= Exp(a + b × 401 – 2 × s)
= Exp(5.2021 + 0.0037 × 401 – 2 × 0.0254)
= Exp(6.6521)
= $774.39
August 14, 2026 calculations
Top border of price channel:
Exp(Y288)
= Exp(a + b × X288 + 2 × s)
= Exp(a + b × 417 + 2 × s)
= Exp(5.2021 + 0.0037 × 417 + 2 × 0.0254)
= Exp(6.8136)
= $910.10
Bottom border of price channel:
Exp(Y288)
= Exp(a + b × X288 – 2 × s)
= Exp(a + b × 417 – 2 × s)
= Exp(5.2021 + 0.0037 × 417 – 2 × 0.0254)
= Exp(6.7120)
= $822.18
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 291.98% per annum.
- CAT price at the close of August 14, 2026 was inside the secondary price channel.