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 59.35% per annum.
- CAT price at the close of September 30, 2026 was $810.79 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.69% per annum.
- CAT price at the close of September 30, 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: June 15, 2026
End date: September 24, 2026
a = 7.7738
b = -0.0025
s = 0.0393
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0025) – 1
= -59.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0393) – 1
= 17.04%
June 15, 2026 calculations
Top border of price channel:
Exp(Y246)
= Exp(a + b × X246 + 2 × s)
= Exp(a + b × 357 + 2 × s)
= Exp(7.7738 + -0.0025 × 357 + 2 × 0.0393)
= Exp(6.9720)
= $1,066.32
Bottom border of price channel:
Exp(Y246)
= Exp(a + b × X246 – 2 × s)
= Exp(a + b × 357 – 2 × s)
= Exp(7.7738 + -0.0025 × 357 – 2 × 0.0393)
= Exp(6.8147)
= $911.11
September 24, 2026 calculations
Top border of price channel:
Exp(Y316)
= Exp(a + b × X316 + 2 × s)
= Exp(a + b × 458 + 2 × s)
= Exp(7.7738 + -0.0025 × 458 + 2 × 0.0393)
= Exp(6.7229)
= $831.19
Bottom border of price channel:
Exp(Y316)
= Exp(a + b × X316 – 2 × s)
= Exp(a + b × 458 – 2 × s)
= Exp(7.7738 + -0.0025 × 458 – 2 × 0.0393)
= Exp(6.5656)
= $710.21
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 59.35% per annum.
- CAT price at the close of September 30, 2026 was $810.79 and was inside the primary price channel.
Secondary Trend
Start date: August 19, 2026
End date: September 30, 2026
a = 6.7030
b = 0.0000
s = 0.0170
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.69%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0170) – 1
= 7.04%
August 19, 2026 calculations
Top border of price channel:
Exp(Y291)
= Exp(a + b × X291 + 2 × s)
= Exp(a + b × 422 + 2 × s)
= Exp(6.7030 + 0.0000 × 422 + 2 × 0.0170)
= Exp(6.7290)
= $836.32
Bottom border of price channel:
Exp(Y291)
= Exp(a + b × X291 – 2 × s)
= Exp(a + b × 422 – 2 × s)
= Exp(6.7030 + 0.0000 × 422 – 2 × 0.0170)
= Exp(6.6610)
= $781.32
September 30, 2026 calculations
Top border of price channel:
Exp(Y320)
= Exp(a + b × X320 + 2 × s)
= Exp(a + b × 464 + 2 × s)
= Exp(6.7030 + 0.0000 × 464 + 2 × 0.0170)
= Exp(6.7282)
= $835.66
Bottom border of price channel:
Exp(Y320)
= Exp(a + b × X320 – 2 × s)
= Exp(a + b × 464 – 2 × s)
= Exp(6.7030 + 0.0000 × 464 – 2 × 0.0170)
= Exp(6.6602)
= $780.69
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.69% per annum.
- CAT price at the close of September 30, 2026 was inside the secondary price channel.