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 43.57% per annum.
- MU price at the close of May 9, 2024 was $117.81 and was higher than the top border of the primary price channel by $15.87 (15.57%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 163.97% per annum.
- MU price at the close of May 9, 2024 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 MU 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: September 13, 2022
End date: March 20, 2024
a = 2.6970
b = 0.0010
s = 0.0590
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.57%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0590) – 1
= 26.62%
September 13, 2022 calculations
Top border of price channel:
Exp(Y842)
= Exp(a + b × X842 + 2 × s)
= Exp(a + b × 1,222 + 2 × s)
= Exp(2.6970 + 0.0010 × 1,222 + 2 × 0.0590)
= Exp(4.0259)
= $56.03
Bottom border of price channel:
Exp(Y842)
= Exp(a + b × X842 – 2 × s)
= Exp(a + b × 1,222 – 2 × s)
= Exp(2.6970 + 0.0010 × 1,222 – 2 × 0.0590)
= Exp(3.7898)
= $44.25
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 + 2 × s)
= Exp(a + b × 1,776 + 2 × s)
= Exp(2.6970 + 0.0010 × 1,776 + 2 × 0.0590)
= Exp(4.5748)
= $97.01
Bottom border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 – 2 × s)
= Exp(a + b × 1,776 – 2 × s)
= Exp(2.6970 + 0.0010 × 1,776 – 2 × 0.0590)
= Exp(4.3388)
= $76.61
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 43.57% per annum.
- MU price at the close of May 9, 2024 was $117.81 and was higher than the top border of the primary price channel by $15.87 (15.57%).
Secondary Trend
Start date: September 21, 2023
End date: May 9, 2024
a = -0.0915
b = 0.0027
s = 0.0665
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0027) – 1
= 163.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0665) – 1
= 30.46%
September 21, 2023 calculations
Top border of price channel:
Exp(Y1,099)
= Exp(a + b × X1,099 + 2 × s)
= Exp(a + b × 1,595 + 2 × s)
= Exp(-0.0915 + 0.0027 × 1,595 + 2 × 0.0665)
= Exp(4.2831)
= $72.47
Bottom border of price channel:
Exp(Y1,099)
= Exp(a + b × X1,099 – 2 × s)
= Exp(a + b × 1,595 – 2 × s)
= Exp(-0.0915 + 0.0027 × 1,595 – 2 × 0.0665)
= Exp(4.0173)
= $55.55
May 9, 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(-0.0915 + 0.0027 × 1,826 + 2 × 0.0665)
= Exp(4.8975)
= $133.95
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-0.0915 + 0.0027 × 1,826 – 2 × 0.0665)
= Exp(4.6316)
= $102.68
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 163.97% per annum.
- MU price at the close of May 9, 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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