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 181.26% per annum.
- CAT price at the close of April 26, 2024 was $343.38 and was lower than the bottom border of the primary price channel by $25.21 (6.84%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 68.79% per annum.
- CAT price at the close of April 26, 2024 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: October 25, 2023
End date: April 15, 2024
a = 0.7978
b = 0.0028
s = 0.0279
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0028) – 1
= 181.26%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0279) – 1
= 11.82%
October 25, 2023 calculations
Top border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 + 2 × s)
= Exp(a + b × 1,640 + 2 × s)
= Exp(0.7978 + 0.0028 × 1,640 + 2 × 0.0279)
= Exp(5.5001)
= $244.71
Bottom border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 – 2 × s)
= Exp(a + b × 1,640 – 2 × s)
= Exp(0.7978 + 0.0028 × 1,640 – 2 × 0.0279)
= Exp(5.3884)
= $218.85
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,249)
= Exp(a + b × X1,249 + 2 × s)
= Exp(a + b × 1,813 + 2 × s)
= Exp(0.7978 + 0.0028 × 1,813 + 2 × 0.0279)
= Exp(5.9902)
= $399.50
Bottom border of price channel:
Exp(Y1,249)
= Exp(a + b × X1,249 – 2 × s)
= Exp(a + b × 1,813 – 2 × s)
= Exp(0.7978 + 0.0028 × 1,813 – 2 × 0.0279)
= Exp(5.8785)
= $357.28
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 181.26% per annum.
- CAT price at the close of April 26, 2024 was $343.38 and was lower than the bottom border of the primary price channel by $25.21 (6.84%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 3, 2024
End date: April 22, 2024
a = 11.6757
b = -0.0032
s = 0.0090
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0032) – 1
= -68.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0090) – 1
= 3.66%
April 3, 2024 calculations
Top border of price channel:
Exp(Y1,241)
= Exp(a + b × X1,241 + 2 × s)
= Exp(a + b × 1,801 + 2 × s)
= Exp(11.6757 + -0.0032 × 1,801 + 2 × 0.0090)
= Exp(5.9478)
= $382.92
Bottom border of price channel:
Exp(Y1,241)
= Exp(a + b × X1,241 – 2 × s)
= Exp(a + b × 1,801 – 2 × s)
= Exp(11.6757 + -0.0032 × 1,801 – 2 × 0.0090)
= Exp(5.9118)
= $369.38
April 22, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(11.6757 + -0.0032 × 1,820 + 2 × 0.0090)
= Exp(5.8872)
= $360.40
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(11.6757 + -0.0032 × 1,820 – 2 × 0.0090)
= Exp(5.8512)
= $347.66
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 68.79% per annum.
- CAT price at the close of April 26, 2024 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.
Check out CAT and 1,499 other stocks on our new website