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 87.95% per annum.
- CAT price at the close of August 3, 2026 was $830.03 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 90.81% per annum.
- CAT price at the close of August 3, 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 22, 2026
End date: August 3, 2026
a = 9.0555
b = -0.0058
s = 0.0294
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0058) – 1
= -87.95%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0294) – 1
= 12.47%
June 22, 2026 calculations
Top border of price channel:
Exp(Y250)
= Exp(a + b × X250 + 2 × s)
= Exp(a + b × 364 + 2 × s)
= Exp(9.0555 + -0.0058 × 364 + 2 × 0.0294)
= Exp(7.0041)
= $1,101.11
Bottom border of price channel:
Exp(Y250)
= Exp(a + b × X250 – 2 × s)
= Exp(a + b × 364 – 2 × s)
= Exp(9.0555 + -0.0058 × 364 – 2 × 0.0294)
= Exp(6.8865)
= $979.01
August 3, 2026 calculations
Top border of price channel:
Exp(Y279)
= Exp(a + b × X279 + 2 × s)
= Exp(a + b × 406 + 2 × s)
= Exp(9.0555 + -0.0058 × 406 + 2 × 0.0294)
= Exp(6.7606)
= $863.16
Bottom border of price channel:
Exp(Y279)
= Exp(a + b × X279 – 2 × s)
= Exp(a + b × 406 – 2 × s)
= Exp(9.0555 + -0.0058 × 406 – 2 × 0.0294)
= Exp(6.6431)
= $767.44
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 87.95% per annum.
- CAT price at the close of August 3, 2026 was $830.03 and was inside the primary price channel.
Secondary Trend
Start date: June 29, 2026
End date: August 3, 2026
a = 9.3468
b = -0.0065
s = 0.0272
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0065) – 1
= -90.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0272) – 1
= 11.51%
June 29, 2026 calculations
Top border of price channel:
Exp(Y255)
= Exp(a + b × X255 + 2 × s)
= Exp(a + b × 371 + 2 × s)
= Exp(9.3468 + -0.0065 × 371 + 2 × 0.0272)
= Exp(6.9754)
= $1,070.01
Bottom border of price channel:
Exp(Y255)
= Exp(a + b × X255 – 2 × s)
= Exp(a + b × 371 – 2 × s)
= Exp(9.3468 + -0.0065 × 371 – 2 × 0.0272)
= Exp(6.8665)
= $959.54
August 3, 2026 calculations
Top border of price channel:
Exp(Y279)
= Exp(a + b × X279 + 2 × s)
= Exp(a + b × 406 + 2 × s)
= Exp(9.3468 + -0.0065 × 406 + 2 × 0.0272)
= Exp(6.7466)
= $851.14
Bottom border of price channel:
Exp(Y279)
= Exp(a + b × X279 – 2 × s)
= Exp(a + b × 406 – 2 × s)
= Exp(9.3468 + -0.0065 × 406 – 2 × 0.0272)
= Exp(6.6376)
= $763.26
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 90.81% per annum.
- CAT price at the close of August 3, 2026 was inside the secondary price channel.