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 173.16% per annum.
- CAT price at the close of May 16, 2024 was $350.72 and was lower than the bottom border of the primary price channel by $34.60 (8.98%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 30.77% per annum.
- CAT price at the close of May 16, 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 19, 2023
End date: April 15, 2024
a = 0.9879
b = 0.0028
s = 0.0305
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0028) – 1
= 173.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0305) – 1
= 12.97%
October 19, 2023 calculations
Top border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 + 2 × s)
= Exp(a + b × 1,616 + 2 × s)
= Exp(0.9879 + 0.0028 × 1,616 + 2 × 0.0305)
= Exp(5.4978)
= $244.16
Bottom border of price channel:
Exp(Y1,114)
= Exp(a + b × X1,114 – 2 × s)
= Exp(a + b × 1,616 – 2 × s)
= Exp(0.9879 + 0.0028 × 1,616 – 2 × 0.0305)
= Exp(5.3759)
= $216.14
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 + 2 × s)
= Exp(a + b × 1,795 + 2 × s)
= Exp(0.9879 + 0.0028 × 1,795 + 2 × 0.0305)
= Exp(5.9906)
= $399.67
Bottom border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 – 2 × s)
= Exp(a + b × 1,795 – 2 × s)
= Exp(0.9879 + 0.0028 × 1,795 – 2 × 0.0305)
= Exp(5.8687)
= $353.79
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 173.16% per annum.
- CAT price at the close of May 16, 2024 was $350.72 and was lower than the bottom border of the primary price channel by $34.60 (8.98%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 20, 2024
End date: May 16, 2024
a = 7.6873
b = -0.0010
s = 0.0280
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -30.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0280) – 1
= 11.83%
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 + 2 × s)
= Exp(a + b × 1,769 + 2 × s)
= Exp(7.6873 + -0.0010 × 1,769 + 2 × 0.0280)
= Exp(5.9610)
= $388.00
Bottom border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 – 2 × s)
= Exp(a + b × 1,769 – 2 × s)
= Exp(7.6873 + -0.0010 × 1,769 – 2 × 0.0280)
= Exp(5.8492)
= $346.95
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.6873 + -0.0010 × 1,826 + 2 × 0.0280)
= Exp(5.9036)
= $366.35
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.6873 + -0.0010 × 1,826 – 2 × 0.0280)
= Exp(5.7918)
= $327.59
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 30.77% per annum.
- CAT price at the close of May 16, 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.
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