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 261.42% per annum.
- CAT price at the close of September 15, 2025 was $435.94 and was lower than the bottom border of the primary price channel by $45.14 (9.38%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.11% per annum.
- CAT price at the close of September 15, 2025 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 3, 2025
End date: August 6, 2025
a = -0.1953
b = 0.0035
s = 0.0265
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0035) – 1
= 261.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0265) – 1
= 11.18%
April 3, 2025 calculations
Top border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 + 2 × s)
= Exp(a + b × 1,660 + 2 × s)
= Exp(-0.1953 + 0.0035 × 1,660 + 2 × 0.0265)
= Exp(5.7012)
= $299.22
Bottom border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 – 2 × s)
= Exp(a + b × 1,660 – 2 × s)
= Exp(-0.1953 + 0.0035 × 1,660 – 2 × 0.0265)
= Exp(5.5952)
= $269.13
August 6, 2025 calculations
Top border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 + 2 × s)
= Exp(a + b × 1,785 + 2 × s)
= Exp(-0.1953 + 0.0035 × 1,785 + 2 × 0.0265)
= Exp(6.1412)
= $464.62
Bottom border of price channel:
Exp(Y1,227)
= Exp(a + b × X1,227 – 2 × s)
= Exp(a + b × 1,785 – 2 × s)
= Exp(-0.1953 + 0.0035 × 1,785 – 2 × 0.0265)
= Exp(6.0352)
= $417.89
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 261.42% per annum.
- CAT price at the close of September 15, 2025 was $435.94 and was lower than the bottom border of the primary price channel by $45.14 (9.38%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: July 16, 2025
End date: September 15, 2025
a = 5.8030
b = 0.0001
s = 0.0214
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0214) – 1
= 8.94%
July 16, 2025 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,764 + 2 × s)
= Exp(5.8030 + 0.0001 × 1,764 + 2 × 0.0214)
= Exp(6.0866)
= $439.92
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,764 – 2 × s)
= Exp(5.8030 + 0.0001 × 1,764 – 2 × 0.0214)
= Exp(6.0010)
= $403.83
September 15, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(5.8030 + 0.0001 × 1,825 + 2 × 0.0214)
= Exp(6.0949)
= $443.60
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(5.8030 + 0.0001 × 1,825 – 2 × 0.0214)
= Exp(6.0093)
= $407.20
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 5.11% per annum.
- CAT price at the close of September 15, 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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